If the Arithmetic Mean (A.M.) and Geometric M | vedclass

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

Question

(D) Let the roots of the quadratic equation be $\alpha$ and $\beta$.Given that the Arithmetic Mean ($A$.$M$.) of the roots is $p$,we have $\frac{\alph

Vedclass · Accepted Answer

$x^{2}-2px+q^{2}=0$

Vedclass · Answer

(D) Let the roots of the quadratic equation be $\alpha$ and $\beta$.Given that the Arithmetic Mean ($A$.$M$.) of the roots is $p$,we have $\frac{\alpha+\beta}{2} = p$,which implies $\alpha+\beta = 2p$.Given that the Geometric Mean ($G$.$M$.) of the roots is $q$,we have $\sqrt{\alpha\beta} = q$,which implies $\alpha\beta = q^{2}$.$A$ quadratic equation with roots $\alpha$ and $\beta$ is given by $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^{2} - (2p)x + q^{2} = 0$,which simplifies to $x^{2} - 2px + q^{2} = 0$.

If the Arithmetic Mean ($A$.$M$.) and Geometric Mean ($G$.$M$.) of the roots of a quadratic equation in $x$ are $p$ and $q$ respectively,then the equation is:

Similar Questions

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

If $3$ distinct real numbers $a, b, c$ satisfy $a^2(a + p) = b^2(b + p) = c^2(c + p)$ where $p \in \mathbb{R}$,then the value of $bc + ca + ab$ is:

If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$,then the quadratic equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is

If $\alpha, \beta, \gamma$ are the real roots of the equation $18x^3-15x^2-4x+4=0$ such that $\alpha=\beta$ and $\alpha>\gamma$,then $\alpha+\beta^2+\gamma^3=$

If $\alpha, \beta$ are the roots of the equation $Ax^2 + Bx + C = 0$ and $\alpha^2, \beta^2$ are the roots of the equation $x^2 + px + q = 0$,then $p = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module