Class 10 Exam > Class 10 Questions > Consider f(x) = 8x4– 2x2+ 6x – 5 ...
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Consider f(x) = 8x4 – 2x2 + 6x – 5 and α,β,γ,δ are it's zeros then α + β + γ + δ =
- a)1/4
- b)-1/4
- c)-3/2
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider f(x) = 8x4– 2x2+ 6x – 5 and α,β,&gamma...
for a equation of 4 roots ax4+bx3+cx2+dx+e=0
sum of roots is -b/a
in our equation b = 0 (since there is no term of x3)
so sum of roots is -b/a=0
Most Upvoted Answer
Consider f(x) = 8x4– 2x2+ 6x – 5 and α,β,&gamma...
Option @ is correct ...... sum of zeroes = -b/a =-(-2)/8 = 2/8 =1/4 ans.............
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Community Answer
Consider f(x) = 8x4– 2x2+ 6x – 5 and α,β,&gamma...
Explanation:
Finding the Sum of Zeros:
To find the sum of the zeros of the given polynomial, we can use the relationship between the coefficients and the roots.
Using Vieta's Formulas:
Vieta's formulas state that for a polynomial of degree n with leading coefficient 1, the sum of the roots taken r at a time is given by (-1)^r * the coefficient of x^(n-r) divided by the leading coefficient.
Applying Vieta's Formulas:
For the given polynomial f(x) = 8x^4 - 2x^2 + 6x - 5, the sum of the zeros is given by:
α + β + γ + δ = -(-2)/8 = 1/4
Comparing with the Options:
The sum of the zeros of the polynomial is 1/4, which matches with option 'D' - None of these.
Therefore, the correct answer is option 'D' - None of these.
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