find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients of x^2-x-72
Answers
x²-x-72
= x²-(9-8)x-72
= x²-9x+8x-72
= x(x-9)+8(x-9)
= (x-9)(x+8)
Therefore,
x - 9 = 0 and x+8 = 0
x = 9 and x = -8
Hence the zeroes are
α = 9
β = -8
α+β = -b/a
α+β = 9-8 = 1
-b/a = -(-1)/1 = 1
αβ = c/a
αβ = 9*-8 = -72
c/a = -72/1 = -72
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ANSWER :–
Roots = - 8 , 9
EXPLANATION :–
GIVEN :–
A quadratic equation x² - x - 72 = 0 have two roots.
To find :–
• Values of roots.
• Verification between the zeroes and coefficients.
SOLUTION :–
● Let's compare given quadratic equation with standard equation ax² + bx + c = 0 .
● So that –
• a = 1
• b = -1
• c = - 72
● Let's find roots –
=> x² - x - 72 = 0
• Now splitting middle term –
=> x² - 9x + 8x - 72 = 0
=> x(x - 9) + 8 (x - 9) = 0
=> (x + 8)(x - 9) = 0
=> x = -8 , x = 9
RELATION VERIFICATION :–
☛ (1) Sum of roots = -b/a
=> -8 + 9 = -(-1/1)
=> 1 = 1 (Verified)
☛ (2) Product of roots = c/a
=> (-8)(9) = (-72/1)
=> -72 = -72 (Verified)