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The quadratic equation whose roots are 3 and -5 is:
x² + 2x - 15 = 0
x² - 2x - 15 = 0
x² - 8x + 15 = 0
x² + 8x - 15 = 0
x² + 2x - 15 = 0
Use the sum (S=−2) and product (P=−15) of roots directly in x2−Sx+P=0.
Roots of the quadratic equation are 3 and -5.
x2−(Sum of roots)x+Product of roots=0
Use the sum (S=−2) and product (P=−15) of roots directly in x2−Sx+P=0.
Forgetting to negate the sum of roots in the quadratic equation formula, leading to the wrong sign for the middle term.
Identify the Roots
Let the given roots be α=3 and β=−5.
α=3,β=−5
Calculate Sum and Product
Find the sum (S) and product (P) of the roots.
S=3+(−5)=−2,P=3×(−5)=−15
Form the Equation
Substitute S and P into the standard formula x2−Sx+P=0.
x2−(−2)x+(−15)=0⟹x2+2x−15=0
A is correct because the quadratic equation formed with sum -2 and product -15 is x² + 2x - 15 = 0.
Understanding the relationship between roots and coefficients is crucial for solving higher-degree polynomial equations and symmetric functions of roots.
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