Question

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and
the coecient
6x² -3- 7x
​

Answer 1

$\large\bf\underline\blue{SolutioN}$

✣ 6x² -3- 7x = 6x² -7x - 3

⇒6x² - (9 - 2)x - 3 = 0

⇒6x² - 9x + 2x - 3 =0

⇒2x (3x + 1) -3 (3x + 1) = 0

⇒(3x + 1) (2x - 3) = 0

Factors of this equation are (3x + 1) (2x - 3)

So, Zeros will be

⇒3x + 1 = 0

⇒3x = -1

$⇒x = \frac{ - 1}{3}$

⇒2x - 3 = 0

⇒2x = 3

$⇒x = \frac{3}{2}$

Verification of zeros :-

Sum of zeros = α + β

= 3/2 + (-1/ 3)

= 9-2/6

= 7/6

=Coefficient of x/Coefficient of x²

Product of zeros = αβ

= 3/2 × (- 1/3)

= -3/6

= Constant term/Coefficient of x²

Hence Zero's are - 1/3 and 3/2