if roots of x 2 +bx+c=0 are real then prove that roots of x 2 +bx+c(x+a)(2x+b)=0 are also real.

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Vikas TU · Answer

x 2 +bx+c = 0 x 2 +bx = -c ---------------------------(1) x 2 +bx+c(x+a)(2x+b)=0 --------------------------(2) put (1) in (2) we get, -c + c[2x^2 +(2a +b)x + ab -1] = 0 c[2x^2 + (2a +b)x + ab -1] = 0 Now c cannot be equal to zero, therefore, 2x^2 + (2a +b)x + ab -1 = 0 and hence roots are real.

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if roots of x 2 +bx+c=0 are real then prove that roots of x 2 +bx+c(x+a)(2x+b)=0 are also real.

if roots of x²+bx+c=0 are real then prove that roots of x²+bx+c(x+a)(2x+b)=0 are also real.

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if roots of x 2 +bx+c=0 are real then prove that roots of x 2 +bx+c(x+a)(2x+b)=0 are also real.

if roots of x2+bx+c=0 are real then prove that roots of x2+bx+c(x+a)(2x+b)=0 are also real.

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if roots of x²+bx+c=0 are real then prove that roots of x²+bx+c(x+a)(2x+b)=0 are also real.