The equation ax2-bx-c-0- where a-b-c are the sides of a - ABC- and the equation x2-2x-1-0 have common roots- The measure of - C is-

The correct option is D 45^∘ condition for common roots a1=b√(2)=c1 Multiplying above equation with √(2) , we get a1√(2)=b1=c1√(2)⇒asin45^o=b ...

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Standard XII

Mathematics

Definition of Functions

The equation ...

Question

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

90^{\circ}

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45^{\circ}

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60^{\circ}

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none of these

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Solution

The correct option is D $45^{\circ}$
condition for common roots
$\frac{a}{1} = \frac{b}{\sqrt{2}} = \frac{c}{1}$

Multiplying above equation with $\sqrt{2}$ , we get

$\frac{a}{\frac{1}{\sqrt{2}}} = \frac{b}{1} = \frac{c}{\frac{1}{\sqrt{2}}} \Rightarrow \frac{a}{s i n 45^{o}} = \frac{b}{s i n 90^{o}} = \frac{c}{s i n 45^{o}}$

Therefore, $C = 45^{o}$

So, Answer is $B$

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The equation ax2+bx+c=0, where a,b,c are the sides of a ΔABC, and the equation x2+√2x+1=0 have common roots. The measure of ∠C is?

The correct option is D 45∘condition for common rootsa1=b√2=c1Multiplying above equation with √2, we geta1√2=b1=c1√2⇒asin45o=bsin90o=csin45oTherefore, C=45oSo, Answer is B

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