Question

find zeroes of the polynomial
$2 {x}^{2} + \: 5x \: - 12$

Also verify relationship between it's zeroes and co efficient

Answer 1

2x^2 + 5x -12 (a=2 ,b=5 ,c=-12)
=2x^2+8x-3x-12
=2x(x+4) -3(x+4)
=(2x-3) (x+4)
now, 2x-3=0
x=3/2= alpha
and,x+4=0
x=-4= bita
we know that,
alpha + bita = -b/a
3/2+(-4)= -5/2
3-8/2= -5/2
-5/2=-5/2

alpha × bita= c/a
3/2×(-4)= -12/2
-12/2=-6
-6=-6
hence ,relationship between its zeroes and coefficient is verified.

hooe it helps:)

Answer 2

Hey there!

$p(x) = 2x {}^{2} + 5x - 12$

By splitting the middle term

$2x {}^{2} + 8x - 3x - 12$

$2x(x + 4) \: - 3(x + 4)$

$(2x - 3)(x + 4)$

$2x - 3 = 0$

$x = \frac{3}{2}$

$x + 4 = 0$

$x = - 4$

verifying relationship between it's zeroes and co efficient

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

$\frac{ - 3}{2} + ( - 4) = \frac{ - 5}{2}$

$\frac{3 - 8}{2} = \frac{ - 5}{2}$

$\frac{ - 5}{2} = \frac{ - 5}{2}$

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

$\frac{3}{2} \times (- 4) = \frac{ - 12}{2}$

$\frac{ - 12}{2} = \frac{ - 12}{2}$

$- 6 = - 6$

Hence, verefied

Glad if helped!