Question

if two rootsof the two quadratic equations x2+mx+1=0 and ax2+bx+a=0 are common, then the value of m are

Answer 1

Answer:

the value of m is b/a for the given problem

Answer 2

Answer:

The value of $m$, when the given two equations  $x^{2} +mx+1 = 0$ and $ax^{2} +bx+a = 0$ have common roots is, $\frac{b}{a}$

Step-by-step explanation:

Given equations,

(a) $x^{2} +mx+1 = 0$

(b) $ax^{2} +bx+a = 0$

Let $\alpha$ and $\beta$ be the common roots.

We know that,

• Sum of roots of a quadratic equation of standard form, $ax^{2} +bx+c =0$ is $-\frac{b}{a}$.
• And the product of roots is $\frac{c}{a}$.

Thus, the sum and product of two roots for,

• Equation (a) are,

            $\alpha + \beta = -\frac{m}{1}$

            $\alpha + \beta = -m$.

Similarly,  $\alpha .\beta$ $= \frac{1}{1}$

                 $\alpha .\beta$$= 1.$

• Equation (b) are,

            $\alpha + \beta = -\frac{b}{a}$

                $\alpha .\beta = \frac{a}{a}$

                $\alpha .\beta = 1$

Therefore, from above equations,

                $-m = -\frac{b}{a}$

                   $m = \frac{b}{a}$

Thus, when the two quadratic equations $x^{2} +mx+1 = 0$ and $ax^{2} +bx+a = 0$ have common roots, $m = \frac{b}{a}$.