Question

Find the zeroes of given quadratic polynom
and verify relation between the zeroes
and its
coefficients.
12x²_18x +40
b) 6x²_13x+6. c)x2-5x+6​

Answer 1

Step-by-step explanation:

ANSWER:-

• We need to find the zeroes of the given polynomials. Starting the question with which the concept is based on:-

$\sf{ \alpha + \beta = \dfrac{-b}{a}}$

In this, alpha and Beta are the sum of the zeroes of polynomial.

$\sf{ \alpha \times \beta = \dfrac{c}{a}}$

In this, alpha and beta are zeroes, and the product of zeroes.

12x²-18x +40

Middle term factorisation:-

12x²- 18x +40

= 2( 6x² - 9x + 20)

This question maybe is incomplete as the required factors cannot be found.

c)x2-5x+6

x² - 2x - 3x + 6

= x(x-2) -3(x-2)

= (x-3)(x-2)

So, 2 factors found are 3 and 2.

Verification:-

$\sf{ \alpha + \beta = \dfrac{-b}{a}}$

$\sf{ 3 +2 | \dfrac{-(-5)}{1}}$

$\sf{ 5 | 5}$ ✔ verified.

$\sf{ \alpha \times \beta = \dfrac{c}{a}}$

$\sf{2 \times 3 | \dfrac{6}{1}}$

$\sf{6 | 6}$ ✔ Verified.

Now,

b) 6x²- 13x+6

= 6x² - 4x - 9x + 6

= 2x (3x-2) -3(3x-2)

(2x-3)(3x-2)

So, these are the zeroes.

Verification- Attachment above.