The equation $a x^{2} + b x + c = 0$ , where a,b,c are the sides of a $△ A B C$ , and the equation $x^{2} + \sqrt{2} x + 1 = 0$ have a common root, the measure of $∠ C$ is

Q. If the equations

a x^{2} + b x + c = 0

and

c x^{2} + b x + a = 0

have one root in common, then

(a + b + c) \times (a - b + c)

equal to:

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If a,b,c be the sides of TriangleABC and equations ax2+bx+c=0 and 5x2+12x+13=0 have a common root, then ∠C is

The correct option is B 90∘ Solution : 5x2+12x+13=0 have complex roots i.e. both root will be common to ax2+bx+c=0 a5=b12=c13=k ∠C=90∘

If $a, b, c$ be the sides of $T r i a n g l e A B C$ and equations $a x^{2} + b x + c = 0$ and $5 x^{2} + 12 x + 13 = 0$ have a common root, then $∠ C$ is

The correct option is B $90^{\circ}$

Solution : $5 x^{2} + 12 x + 13 = 0$ have complex roots i.e. both root will be common to $a x^{2} + b x + c = 0$
$\frac{a}{5} = \frac{b}{12} = \frac{c}{13} = k$
$∠ C = 90^{\circ}$