Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
(i) 1/4, - 1   (ii) √2, 1/3   (iii) 0, √5   (iv) 1, 1   (v) - 1/4, 1/4
(vi) 4, 1

Solution:

The sum of roots and the product of roots are given. We have to form a quadratic polynomial.

Put the values in the general equation of the quadratic polynomial , that is k [x² - (sum of roots) x + (product of roots)] where k is any real number.

Let's assume k = 1 in each case.

(i) 1/4, - 1

We know that the general equation of a quadratic polynomial is:

x² - (sum of roots) x + (product of roots)

x² - (1/4)x + (- 1)

x² - (1/4)x - 1

(ii) √2, 1/3

We know that the general equation of a quadratic polynomial is:

x² - (sum of roots) x + (product of roots)

x² - √2 x + 1/3

(iii) 0, √5

We know that the general equation of a quadratic polynomial is:

x² - (sum of roots) x + (product of roots)

x² - 0 x + √5

x² + √5

(iv) 1, 1

We know that the general equation of a quadratic polynomial is:

x² - (sum of roots) x + (product of roots)

x² - 1x + 1

x² - x + 1

(v) - 1/4, 1/4

We know that the general equation of a quadratic polynomial is:

x² - (sum of roots) x + (product of roots)

x² - (- 1/4)x + 1/4

x² + (1/4)x + 1/4

(vi) 4, 1

We know that the general equation of a quadratic polynomial is:

x² - (sum of roots) x + (product of roots)

x² - 4x + 1

☛ Check: NCERT Solutions Class 10 Maths Chapter 2

---

Video Solution:

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) 1/4, - 1 (ii) √2, 1/3 (iii) 0, √5 (iv) 1, 1 (v) - 1/4, 1/4 (vi) 4, 1 

NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.2 Question 2

Summary:

The quadratic polynomials for the given numbers as the sum and product of the polynomials are i) x² - (1/4)x - 1, ii) x² - √2 x + 1/3, iii) x² + √5, iv) x² - x + 1, v) x² + (1/4)x + 1/4 and vi) x² - 4x + 1 respectively.

---

☛ Related Questions:

• The graphs of y = p(x) are given in the figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
• Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients(i) x2 - 2x - 8(ii) 4s2 - 4s + 1(iii) 6x2 - 3 - 7x(iv) 4u2 + 8u(v) t2 - 15(vi) 3x2 - x - 4
• Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) p(x) = x3 - 3x2 + 5x - 3, g(x) = x2 - 2(ii) p(x) = x4 - 3x2 + 4x + 5, g(x) = x2 + 1 - x(iii) p(x) = x4 - 5x + 6, g(x) = 2 - x2
• Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:(i) t2 - 3, 2t4 + 3t3 - 2t2 - 9t - 12(ii) x2 + 3x + 1, 3x4 + 5x3 - 7x2 + 2x + 2(iii) x3 - 3x + 1, x5 - 4x3 + x2 + 3x + 1