Question

Find the zeroes of the quadratic polynomial x² + x - 12 and verify the relationship between the zeroes and
the coefficients. ​

Answer 1

Step-by-step explanation:

ANSWER:-

Given Polynomial:-

${x}^{2} + x - 12$

To find the Zeroes, We need to factorise by

Middle Term Factorisation

Factors of 12 Applicable is 3 and 4

${x}^{2} + 4x - 3x - 12$

$x(x + 4) - 3(x + 4)$

$(x - 3)(x + 4)$

So the zeroes are

$x = 3$

$\alpha = 3$

$x = - 4$

$\beta = - 4$

Verification

We know that

$\alpha + \beta = \frac{ - b}{a}$

$\alpha \beta = \frac{c}{a}$

So, we know that

b = 1 , a = 1 and c = -12

Placing Zeroes,

$\alpha + \beta = 3 + ( - 4)$

$= - 1$

Now ,

$\frac{ - b}{a} = \frac{ - 1}{1}$

Verified

Now with products,

$\alpha \beta = 3 \times ( - 4) = - 12$

$\frac{c}{a} = \frac{ - 12}{1} = - 12$

Hence Verified!!