Question

The equation whose roots are the squares of the roots of the equation
$2x^2+3x+1=0$ is

• A. 4x² +5x + 1 = 0
• B. 4x² - 5x + 1 = 0
• C. 5x² - 4x + 1 = 0
• D. 4x² - 9x + 1 = 0

Answer 1

The correct option is B

4x² - 5x + 1 = 0

Let a and b are the roots of the equation $2x^2+3x+1=0$
For a quadratic equation $a{x}^2+bx+c=0,$
Sum of roots $=-\frac{b}{a}$ Product of roots $=\frac{c}{a}$
Then,
Sum of the roots, a + b $=-\frac{3}{2}$
Product of the roots, a + b $=-\frac{1}{2}$
We have to find the equation whose roots are $a^{2}and{b}^2$
Sum of the roots $=a^2\times b^2=(ab{)}^2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$
So, the new equation with roots $a^{2}and{b}^2$
$x^2-\frac{5}{4}x+\frac{1}{4}=0multiplyingby4gives,4x^2-5x+1=0$
$4x^2-5x+1=0$