Question

Find the zeros of the quadratic polynomial $5x^2+12x+7$ and
verify the relation between the zeros and the coefficient.

Answer 1

Consider the given polynomial $f\left(x\right)=5x^2+12x+7$

Find the zeros that

$\Rightarrow 5x^2+12x+7=0$

$\Rightarrow 5x^2+(7+5)x+7=0$

$\Rightarrow 5x^2+7x+5x+7=0$

$\Rightarrow 5x^2+5x+7x+7=0$

$\Rightarrow 5x(x+1)+7(x+1)=0$

$\Rightarrow (x+1)(5x+7)=0$

$\Rightarrow x+1=05x+7=0$

$\Rightarrow x=-1andx=-\frac{7}{5}$

Hence, this is the answer.

Verifythe relation between the zeros and the coefficient.

We know that,

Sum of zeros$=-\frac{cofficentofx}{cofficentof{x}^2}$

$\Rightarrow -1+(-\frac{7}{5})=-\frac{12}{5}$

$\Rightarrow -\frac{12}{5}=-\frac{12}{5}$

Now, product of zeros$=-\frac{cons\tan t}{cofficentof{x}^2}$

$\Rightarrow -1\times (-\frac{7}{5})=\frac{7}{5}$

$\Rightarrow \frac{7}{5}=\frac{7}{5}$

Hence, this the complete solution.