Question

If one zero of quadratic polynomial 4x^2-8kx+8x-9 is negative of other then find zeroes of kx^2+3kx+2

Answer 1

hope it will help you

Answer 2

Answer:

The zeroes are -1 and -2

Step-by-step explanation:

$\text{Given that one zero of quadratic polynomial }4x^2-8kx+8x-9 \text{ is negative of other then}$

$\text{we have to find the zeroes of }kx^2+3kx+2$

$\text{ As one zero of quadratic polynomial }4x^2-8kx+8x-9 \text{ is negative of other }$

∴ let the zeroes are α and -α

$\text{sum of roots= }\alpha+(-\alpha)=\frac{-b}{a}=\frac{-(-8k+8)}{4}$

⇒ $\frac{-(-8k+8)}{4}=0$

⇒ $\frac{8k-8}{4}=0$

$8k-8=0$

$k=1$

The polynomial becomes

$(1)x^2+3(1)x+2$

$x^2+3x+2$

$x^2+2x+x+2$

$x(x+2)+1(x+2)$

$(x+1)(x+2)$

x+1=0  ⇒ x=-1

x+2=0  ⇒ x=-2

Hence, the zeroes are -1 and -2