if alpha and beta are zeros of the quadratic polynomial p x is equal to 4 x square - 5 x minus 1 find the value of Alpha square plus alpha beta square
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Secondary School Math 5 points
If alpha and beta are the zeros of quadratic polynomial p(x)=4x2-5x-1,find the value of alpha square beta+ alpha beta square
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ALTAF11
ALTAF11 Ace
Hey!
Given polynomial :- 4x²-5x-1
and alpha beta are it's zeros !
• Sum of Zeros =
= \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }
\alpha + \beta = \frac{5}{4}
• Product of Zeros =
\frac{constant \: term}{coeff. \: \: of \: {x}^{2} }
\alpha \beta = \frac{ - 1}{4}
# To find
{ \alpha }^{2} \beta + \alpha { \beta }^{2}
\alpha \beta ( \alpha + \beta )
\frac{ - 1}{4} \times \frac{5}{4} = \frac{ - 5}{16}
Hence , value is -5/16
Answer:
p(x)= 4x^2-5x-1
Sum of zeroes= -b/a = 5/4
Product of zeroes= -1/4
(alpha)^2.beta + alpha(beta)^2
alpha.beta (alpha+ beta)
-1/4(5/4)
-5/16