Question

1. If one zero of the quadratic polynomial $x^2-7x+5k$ is $-2$, then find the value of $k.$
2. Find the value of ${}^{\prime }{c}^{\prime }$ for which the pair of equation $cx+2y=3$ and $12x+8y=12$ will have infinite solutions.

Answer 1

$1.$ $x^2-7x+5k=0$

One of the root $=-2$

$\alpha +\beta =7$

$\alpha \beta =5k$

If, $\alpha =-2,\beta =9$

$\therefore k=\frac{(-2)\left(9\right)}{5}=\frac{-18}{5}$

$k=\frac{-18}{5}$

$2.$ $cx+2y=3$ (Equation $01$)

$12x+8y=12$ (Equation $02$)

$a_1=c$ $b_1=12$

$a_2=2$ $b_2=8$

$a_3=3$ $b_3=12$

For infinitetly set,

$\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}$

$\frac{c}{12}=\frac{1}{4}=\frac{1}{4}$

$\therefore c=3$