Question

with the help of diagi
Find the zeroes of the quadratic polynomial P(x) = x2 + x-12 and
verify the relationship between the zeroes and the coefficients.​

Answer 1

Question -: find the zeroes of the quadratic polynomial P(x) = x2 + x-12 and

verify the relationship between the zeroes and the coefficients.

let's try to solve the question

firstly we will factorise the given polynomial

let' s factorise

$\dashrightarrow \: {x}^{2} + x - 12 = 0$

$\dashrightarrow \: {x}^{2} + 4x - 3x - 12 = 0$

$\dashrightarrow \:x(x + 4) - 3(x + 4) = 0$

$\dashrightarrow \: (x + 4)(x - 3) = 0$

$x = - 4 \: and \: x = 3$

Now we have

$\alpha = - 4 \: and \: \beta = 3$

and a = 1

b = 1

and c = -12

let's verify the relationship among the zeros

$sum \: of \: zeros \: \\ \alpha + \beta = \frac{ - b} - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {a}$

$- 4 + 3 = - 1$

$lhs \: = \: rhs$

also product of zeros

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

$- 4 \times 3 = - 12$

$lhs \: = rhs$

Hence verified

Hope this will help you

Thank you ..

Answer 2

Answer

alpha=3 and beta= -4

by putting the we can get answers