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 $\alpha, \beta$ are the roots of $x^2-5 \gamma x-6 \delta=0$ and $\gamma, \delta$ are the roots of $x^2-5 \alpha x-6 \beta=0$,then $\alpha+\beta+\gamma+\delta=$

If $\alpha, \beta$ are the roots of the equation $x^2 - 6x - 2 = 0$,$\alpha > \beta$ and $a_n = \alpha^n - \beta^n$,$n > 1$,then the value of $\frac{a_{10} - 2a_8}{2a_9}$ is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-9x^2+23x-15=0$,then $\alpha^3+\beta^3+\gamma^3=$

The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is

If the arithmetic mean and geometric mean of the two roots of a quadratic equation are $9$ and $4$ respectively,then what is the quadratic equation?

Vedclass Test Series

Exam Paper Generator

Online Exam Module