Tough questions of Quadratic Polynomials class 10th.

Tough and Hot Questions of Quadratic Polynomials Class 10th.

Do you find tough questions of quadratic polynomials? Do you search for the important questions of quadratic polynomials? Do you want to know how to deal with tough questions? Do you find important questions based on relations between zeros and coefficients of quadratic polynomials? Then, you are at the right place.

In this article, I shall guide you on how to solve word problem questions in easy ways. Our team made it so easy to learn very soon. I hope solutions to all questions provide unique ideas and clear all doubts regarding these topics. Do you have any relevant doubts regarding this topic? You should consult with our expert teams at any time.

You should know some important algebraic formulas before understanding the quadratic polynomials questions. These formulas are essential for better understanding. No doubt without these formulas, any solutions of quadratic polynomials are possible.

Applying these formulas to questions reduces your stress regarding tough questions.

Let's understand each important formula.

Important Questions Based on Quadratic Polynomial Chapter 2.

These questions are tough and related to the previous year. they are important for your upcoming examination. These questions are asked frequently by students to our experts. Every year students say that we get only doubt about algebraic formulas. How to put these values in equations based on the relationship between zeroes and the coefficient of Quadratic polynomial.

Here, we have published an online solution for quadratic polynomials of previous years. It will help you get the right strategies for the upcoming CBSE board examination. These solutions of quadratic polynomials are digestible for every student. I hope it helps you more than you expected. 

Do you think the questions are the exact match of the previous year's papers or not?

Absolutely, these questions are picked from previous year's question papers. The last year's questions start from question no 19. Confidently, you can begin your learning process without any hesitation.

Why previous years' questions of quadratic polynomials are important for us?

1. These questions help to understand the trend of questions in board examinations.
2. These questions help to improve the practice regarding Chapter 2.
3. These questions help to relate to the difficulties of repeated questions.

Let us understand one by one.

Question 1 Find the zeroes of the polynomial f(t) = 4t²+8t, and verify the relationship between the zeroes and its coefficients.

Solution:

Question 2 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²+7x+12, then find the values of (1) 𝝰²+𝞫² and (2) 1/𝞪 +1/𝞫.

Solution:

Question 3 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = ax²+bx+c, then find the value of 

(1) 𝛃/𝜶+𝜶/𝛃      (2) 𝜶³+𝛃³        (3) 1/𝜶³+1/𝛃³       

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = ax²+bx+c,

 (4) 𝝰²/𝛃+𝞫²/𝜶 

Solution:

Question 4 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = ax²+bx+c, then find the value of  (1)  𝜶⁴+𝞫⁴

Solution:

(2)     𝝰²/𝛃²+𝞫²/𝜶² 

Question 5 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²-5x+k, such that 𝜶-𝞫=1, find the value of k.

Solution: 

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²-5x+k.

Question 6 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = kx²+4x+4, such that 𝜶²+𝞫²=24, find the value of k.

Solution:

 Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = kx²+4x+4,

  f(x) = kx²+4x+4,

Question 7 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 2x²+5x+k, satisfying the relation  𝜶²+𝞫²+𝜶𝞫=21/4, then find the value of k for this to be possible.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 2x²+5x+k,

Question 8 If the sum of the squares of the zeroes of the Quadratic polynomial f(x) =  x²-8x+k is 40, find the value of k.

Solution:

Let 𝝰 and 𝞫 be the zeroes of the quadratic polynomial f(x) = x²-8x+k is 40,

Then,

Question 9 Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax²+bx+c, c≠0, a≠0.

Solution:

Let 𝝰 and 𝞫 be the zeroes of the quadratic polynomial f(x) = ax²+bx+c.

Then,

Question 10 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 2x²-5x+7, Find a polynomial whose zeroes are 2𝝰+3𝞫 and 2𝝰+3𝞫.

Solution: 

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 2x²-5x+7.

Question 11 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 4x²-5x-1, Find the value of 𝝰²𝞫+𝝰𝞫².

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 4x²-5x-1, 

Question 12 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(t) = t²-4t+3, Find the value of 𝝰⁴𝞫³+𝝰³𝞫⁴.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(t) = t²-4t+3,

Question 13 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²-5x+4, Find the value of 1/𝝰+1/𝞫-2𝜶𝞫.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²-5x+4,

Question 14  If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 3x²-6x+4, Find the value of 𝞫/𝝰+𝜶/𝞫-2(1/𝜶+1/𝞫)+3𝜶𝞫.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 3x²-6x+4,

Question 15 If 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²-px+q, 

Question 16 If the squared difference of the zeroes of the quadratic polynomial f(x)=  x²+px+45 is equal to 144, find the value of p.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = x²+px+45,

Question 17 If the sum of the zeroes of the quadratic polynomial f(x)= kx²+2x+3k is equal to their product, find the value of k.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = kx²+2x+3k,

Question 18 If one zero of the quadratic polynomial f(x)= 4x²- 8kx-9 is negative of the other, find the value of k.

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 4x²-8kx-9,

Question 19 If (x+a) is the factor of f(x)= 4x²+ 2ax+5x+10, find the value of a.

Solution:

Question 20 For what value of k, -4 is a zero of the polynomial x² - x - (2k+2)?

Solution:

Question 21 If 1 is a zero of the polynomial f(x)= ax²-3(a-1)x-1, then find the value of a.

Solution:

Question 22 If the sum of zeroes of the polynomial p(x) = 2x² - k√2x+1 is √2, then value of k is:

Solution:

Question 23 If the sum and product of the zeroes of a quadratic polynomial are 2√3 and 3 respectively, then a quadratic polynomial is:

Solution: 

Question 24 The zeroes of a polynomial x²+px+q are twice the zeroes of the polynomial 4x²+-5x-6. The value of p is:

Solution: 

Question 25 If 𝜶 and 𝞫 are zeroes of the polynomial 5x²+3x–7, the value of 1/𝜶+1/𝞫 is:

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 5x²+3x–7,

Question 26  If 𝜶 and 𝞫 are zeroes of the polynomial 2x²-9x+5, then the value of  𝜶²+𝞫² is:

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = 2x²-9x+5,

Question 27 If 𝜶 and 𝞫 (𝝰 >𝞫) are zeroes of the polynomial -x²+8x+9, then the value of  𝜶-𝞫 is:

Solution:

Since 𝝰 and 𝞫 are the zeroes of the quadratic polynomial f(x) = -x²+8x+9, 

Question 28 If a polynomial p(x) is given by p(x)= x²-5x+6, then the value of p(1)+P(4) is:

Solution:

Question 29 A quadratic polynomial, one of whose zeroes is 2+√5 and the sum of whose zeroes is 4, is:

Solution:

Let 𝝰 and 𝞫 be the zeroes of the quadratic polynomial f(x), 

Question 30 For what value of k, the product of zeroes the polynomial kx²-4x-7 is 2?

Solution:

Let 𝝰 and 𝞫 be the zeroes of the quadratic polynomial f(x)= kx²-4x-7,

 Conclusion:

I have provided hot questions related to Quadratic Polynomials and digestible solutions. I hope you learn easily. Most of the questions are based on the algebraic formulas that are listed above. if you have any doubts regarding solutions, you can contact us immediately right now. Our expert reach you very soon.