Question

Find the nature of the roots of the following quadratic equations . If the real roots exit. find them:

1) $2x^2-3x+5=0$

2) $3x^2-\sqrt[4]{43}x+4=0$

Answer 1

Solution:-

Given quadratic equations

(i) $2x^2-3x+5=0$

comparing with the general equation of quadratic

$a{x}^2+bx+c,$ we get $-a=2$ $b=-3$ $c=5$

$\therefore D=b^2-4ac=9-40<0$

$\Rightarrow$ Imaginary roots

(ii) $3x^2-\sqrt[4]{43}x+4=0$

comparing with general quadratic equation

$a=3$ $b=\sqrt[4]{43}$ $c=4$

$\therefore D=b^2-4ac=\sqrt{3}-48<0$

$\Rightarrow$ Imaginary roots