"If the value of real number $a0$ for which $x^2-5 a x+1=0$ and $x^2-a x-5=0$ have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $\beta$ is equal to ___________."

Question

Accepted Answer

"

${x^2} - 5\alpha x + 1 = 0$ ..... (1)

${x^2} - \alpha x - 5 = 0$ ...... (2)

have a common root.

Subtracting (1) with (2) we'll get $x = {6 \over {4\alpha }}$

Substituting in (1)

${{36} \over {16{\alpha ^2}}} - {{30} \over 4} + 1 = 0$

$\Rightarrow {\alpha ^2} = {9 \over {26}}$

$\alpha = {3 \over {\sqrt {2 \times 13} }}$

$\therefore$ $\beta = 13$

"

If the value of real number $a>0$ for which $x^2-5 a x+1=0$ and $x^2-a x-5=0$

have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $\beta$ is equal to ___________.

Solution

About this question

Drill 25 more like these. Every day. Free.

If the value of real number $a>0$ for which $x^2-5 a x+1=0$ and $x^2-a x-5=0$ have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $\beta$ is equal to ___________.

Solution

About this question

More Complex Numbers and Quadratic Equations questions

Drill 25 more like these. Every day. Free.

If the value of real number $a>0$ for which $x^2-5 a x+1=0$ and $x^2-a x-5=0$

have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $\beta$ is equal to ___________.