Equatioñ

Algebra Level 3

If coefficients of biquadratic equation are all distinct and belong to the set { − 9 , − 5 , 3 , 4 , 7 } \{-9,-5,3,4,7\} , then equation has:

None of these choices 4 real roots, 2 are conjugate surds & other 2 are also conjugate surds 4 imaginary roots At least 2 real roots

Vedant Sharda by Vedant Sharda , 20, India

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1 solution

Vedant Sharda
Jan 16, 2016

Let a biquadratic equation f(x)= ax⁴+bx³+cx²+dx+e

Then a+b+c+d+e = -9-5+3+4+7 = 0

So, at x= 1, f(x) = 0 (1 real root) remaining 3 cannot be imaginary so at least 2 real root

4 Helpful 0 Interesting 0 Brilliant 0 Confused

I don't understand your question and solution.

A biquadratic equations is a quartic equation having no odd powers.

Pi Han Goh - 5 years, 4 months ago

How remaining two cannot be imaginary ?

Ramendra Polai - 5 years, 4 months ago

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Remaining 3 cannot be imaginary as imaginary roots occur in conjugate pair

so atleast 2 real root

Vedant Sharda - 5 years, 4 months ago

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