One common root is okay

Algebra Level 5

True/False?

If the quadratic equations a x 2 + b x + c = 0 ax^2+bx+c=0 and p x 2 + q x + r = 0 px^2+qx+r=0 have a common root and the equation a x 2 + b x + c = 0 ax^2+bx+c=0 has non-real roots, then the given equations have both the roots common.

False True

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

It is true that imaginary roots always exists in pair provided that coefficients are real. Here, nothing is specified about real coefficients, so we can't conclude anything.

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Real coefficients, not real roots.

Vishwak Srinivasan - 5 years, 11 months ago

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Thanks, I've edited the solution

Prakash Chandra Rai - 5 years, 11 months ago

It should have real coefficients otherwise it won't be a quadratic eqn. Ur soln is not correct.

Abhimanyu Gulia - 5 years, 11 months ago

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So according to you, what is a definition of quadratic equation. Where it is mentioned that coefficients can't be real.

According to me, any second degree polynomial equation is a quadratic equation. Mention your definition.

Prakash Chandra Rai - 5 years, 11 months ago
Ravi Dwivedi
Jul 4, 2015

It is not given that a,b,c,p,q,r are real numbers.Hence the statement is not true

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