Form a quadratic equations whose roots are -4 and 5 Select one: a. x2-x+20=0 b. x2-x-20=0 c. 4x2-x-20=0 d. x2+9x-20=0
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Answer :
b) x² - x - 20= 0
The general formula of a quadratic equation can be given by :
P(x) = kx² - (sum of the roots )x + product of the roots
Where k is any constant like 1 , 2 , 3 , etc .
Given :
- The roots of the quadratic equation are - 4 and 5 .
Solution :
Sum of the roots = -4 + 5
= 1
Product of the roots = -4 × 5
= -20
Equation :
P(x ) = k x² - (1) x + (-20)
P(x) = kx² - x -20
Let P(x) = 0 and K = 1
0 = x² - x -20
or
x² - x -20 = 0
Verification :
Solving the equation by middle term splitting :
x² - x -20 = 0
x² - (5-4) x -20 = 0
x² - 5x +4x -20=0
x(x-5) + 4(x -5)= 0
(x+4) (x-5)= 0
x+4 = 0
x = -4
and
x-5 = 0
x = 5
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