Question

The equation ax2+bx+c=0, where a,b,c are the sides of a △ABC, and the equation x2+√2x+1=0 have a common root, the measure of ∠C is 90° 45° 60° None of these

Solution

The correct option is D None of these Clearly, the roots of x2+√2x+1=0 have imaginary roots, so one root common implies both roots are common So, a1=b√2=c1=k ∴cos C=a2+b2−c22ab=k2+2k2−k22k√2k=1√2 ⇒∠C=45o

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