Question

49. If the roots of the quadratic equation are 3 and 5 -2, then the quadratic equation will be (1) x2 + x-6 = 0 (2) x2 + x + 6 = 0 (3) x2 - X-6 = 0 (4) x2 - X+6 = 0 hinh the quadra 1​

Answer 1

Question:

• If the roots of the quadratic equation are *3 and -2. then the quadratic equation will be?

a) x² + x - 6 = 0

b) x² + x + 6 = 0

c) x² - x - 6 = 0

d) x² - x + 6 = 0

Solution:

Let the quadratic equation be ax² + bx + c = 0 where a and b are the coefficients of x² and x respectively.

Now, we are given the zeroes of this quadratic equation as 3 and -2. As we have studied earlier:

A quadratic equation is expressed in the form x² - (Sum of zeroes)x + (Product of zeroes)

> x² - [ 3 + (-2) ] x + ( 3 × 2 ) = 0

> x² - ( 3 - 2 )x + 6 = 0

> x² - x + 6 = 0

Hence, The required quadratic equation is x² - x + 6 = 0 and therefore Option (d) is the correct answer.