If alpha and beta are the roots of the equati | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation $2x^2 - 3x + 4 = 0$,the sum of the roots is $\alpha + \beta = -(-3)/2 = 3/2$ and the product of the roots is $\alpha\beta = 4/2

Vedclass · Accepted Answer

$4x^2 + 7x + 16 = 0$

Vedclass · Answer

(B) Given the equation $2x^2 - 3x + 4 = 0$,the sum of the roots is $\alpha + \beta = -(-3)/2 = 3/2$ and the product of the roots is $\alpha\beta = 4/2 = 2$.The sum of the new roots is $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = (3/2)^2 - 2(2) = 9/4 - 4 = (9 - 16)/4 = -7/4$.The product of the new roots is $\alpha^2\beta^2 = (\alpha\beta)^2 = (2)^2 = 4$.The required quadratic equation is $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^2 - (-7/4)x + 4 = 0$,which simplifies to $x^2 + 7/4x + 4 = 0$.Multiplying by $4$,we get $4x^2 + 7x + 16 = 0$.

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x + 4 = 0$,then the equation whose roots are $\alpha^2$ and $\beta^2$ is

Similar Questions

If $\alpha, \beta$ are the roots of the equation $x^2+bx+c=0$ and $\alpha+h, \beta+h$ are the roots of the equation $x^2+qx+r=0$,then $h$ is equal to

If $\alpha, \beta$ are the roots of the equation $x^2+5x+2=0$,then $\left(\frac{\alpha}{2+5\alpha}\right)^2+\left(\frac{\beta}{2+5\beta}\right)^2=$

Let $a, b \in \mathbb{C}$. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta - \alpha = \sqrt{11}i$ and $\beta^2 - \alpha^2 = 3\sqrt{11}i$, then $(\beta^3 - \alpha^3)^2$ is equal to:

If $(\alpha+\sqrt{\beta})$ and $(\alpha-\sqrt{\beta})$ are the roots of the equation $x^{2}+px+q=0$, where $\alpha, \beta, p$ and $q$ are real, then the roots of the equation $(p^{2}-4q)(p^{2}x^{2}+4px)-16q=0$ are

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module