If x^2 - hx - 21 = 0 and x^2 - 3hx + 35 = 0 ( | vedclass

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(D) Let $\alpha$ be the common root of the two equations.Then,$\alpha^2 - h\alpha - 21 = 0$  $(1)$And $\alpha^2 - 3h\alpha + 35 = 0$  $(2)$Subtracting

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Let $\alpha$ be the common root of the two equations.Then,$\alpha^2 - h\alpha - 21 = 0$  $(1)$And $\alpha^2 - 3h\alpha + 35 = 0$  $(2)$Subtracting equation $(1)$ from equation $(2)$,we get:$(\alpha^2 - 3h\alpha + 35) - (\alpha^2 - h\alpha - 21) = 0$$-2h\alpha + 56 = 0$$2h\alpha = 56$$h\alpha = 28$$\alpha = \frac{28}{h}$Substitute $\alpha = \frac{28}{h}$ into equation $(1)$:$(\frac{28}{h})^2 - h(\frac{28}{h}) - 21 = 0$$\frac{784}{h^2} - 28 - 21 = 0$$\frac{784}{h^2} = 49$$h^2 = \frac{784}{49} = 16$Since $h > 0$,we have $h = 4$.

If $x^2 - hx - 21 = 0$ and $x^2 - 3hx + 35 = 0$ $(h > 0)$ have a common root,then the value of $h$ is equal to

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