Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.(i)6x^2+7x+2(ii)4x^2-4x-3

Answer 1

Answer:

Step-by-step explanation:

Answer 2

(i) 6x^2 + 7x + 2

here, a = 6 , b = 7 & c = 2

D = b^2 - 4ac

D = 7^2 - 4 × 6 × 2 = 49 - 48 = 1

D = 1 > 0

So, roots are real and distinct.

$\alpha = \frac{ - b + \sqrt{d} }{2a}$

$\alpha = - \frac{ - 7 + \sqrt{1} }{2 \times 6}$

$\alpha = \frac{ - 7 + 1}{12}$

$\alpha = \frac{ - 6}{12}$

$\alpha = - \frac{1}{2}$

&

$\beta = \frac{ - b - \sqrt{d} }{2a}$

$\beta = \frac{ - 7 - \sqrt{1} }{2 \times 6}$

$\beta = \frac{ - 7 - 1}{12}$

$\beta = \frac{ - 8}{12}$

$\beta = - \frac{2}{3}$

Verification:

sum of roots = a + b = (-1/2) + (-2/3) = -7 / 6 = -b / a.

Product of roots = ab = (-1/2)×(-2/3) = 1/3 = 1/3 × 2/2 = 2/6 = c / a.

Similarly do the second one.