Question

Find zeroes of the following Quadratic polynomial
and verify the relation between the zeroes
and their coefficients
x2+ 13x-30
3x2 -10 X +8
x^-9
7x^2 - 84

​

Answer 1

Given =》

1) x²+13x-30

2)3x²-10x+8

3)x²-9

4)7x²-84

Solution =》

1) x²+13x-30

Let p(x)= x²+13x-30=0

x²+(15-2)x-30=0

x²+15x-2x-30=0

x(x+15)-2(x+15)=0

(x+15)(x-2)=0

(x+15)=0,(x-2)=0

x=-15, x=2

Sum of zeros = - coefficient of x/ coefficient of x²

=-15+2 = -b/a

$- 13 = \frac{ - 13}{1} \\ = - 13 = - 13$

Product of zeros = constant term / coefficient of x²

= -15×2 =c/a

=

$- 30 = \frac{ - 30}{1} \\ = - 30 = - 30$

Hence verified!

2) 3x²-10x+8

Let p(x) = 3x²-10x+8=0

3x²-(6+4)x+8=0

3x²-6x-4x+8=0

3x(x-2)-4(x-2)=0

(x-2)(3x-4)=0

(x-2)=0, (3x-4)=0

x=2, 3x=4

x=4/3

Sum of zeros =- b/a

$2 + \frac{4}{3} = \frac{ - ( - 10)}{3} \\ = \frac{10}{3} = \frac{10}{3}$

Product of zeros = c/a

$2 \times \frac{4}{3} = \frac{8}{3} \\ = \frac{8}{3} = \frac{8}{3}$

Hence verified!

3)x²-9

Let p(x) = x²-9=0

${x}^{2} - ( \sqrt{9} ) {}^{2} \\ = (x + \sqrt{9} )(x - \sqrt{9} ) = 0 \\ = x + \sqrt{9 } = 0 \: . \: x - \sqrt{9} = 0 \\ = x = - \sqrt{9} . \: x = \sqrt{9}$

Sum of zeros = -b/a

-√9+√9= 0/1

0=0

product of zeros = c/a

=-√9×√9= -9/1

-9=-9

Hence verified!