Find the polynomial whose sum of its zeroes is -8/5 and the product of the zeroes is 7/5.
A) 14x^2+7x+5
B) 5x^2+8x+7
C) 2x^2-8×+7
D) 5x^2-8x+7
Answers
⭐Hey There⭐
Here's your answer ⤵
⭐Sum of the roots = α + β = -8/5⭐
⭐Product of the roots = αβ = 7/5⭐
⭐Given that the general quadratic equation can be written as:
=> x² - (α + β)x + αβ
⭐Sub α + β = -8/5 and αβ = 7/5:
=>Ωx² - (α + β)x + αβ
=> x² - (-8/5)x + (7/5)
=> 5x² + 8x + 7
Answer: (B) 5x² + 8x + 7
⭐Thanks for asking the question !!
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HEY THERE!!
Method Of Solution:-
Given:
Sum of its Zeroes = -8/5
Product of its Zeroes = 7/5
•°• Now,
Sum of Zeroes = -b/a = -(Coefficient of x²)/Coefficient of x
Product of Zeroes = c/a = (Coefficient of x)/Constant term.
Now, Considering on Question Statement!!
General Formula of Quardratic Polynomial
=> ax²-(a+b)x + ab
Substitute the Given Value in Equation!
ax²-(a+b)x +ab
f(x) = 0
•°• x²-(a+b)x + ab = 0
=> x²-(-8/5)x + 7/5 =0
=> x²+8/5x + 7/5 = 0
=>5x²+8x+7/5 = 0
=> 5x²+8x+7= 0
Hence, Quadratic Polynomial => 5x²+8x+7
Here, Option B is Correct Answer.
Thank You!!