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The quadratic equation whose roots are 2 and -3 is:
x² - x - 6 = 0
x² + x - 6 = 0
x² - 5x + 6 = 0
x² + 5x - 6 = 0
x² + x - 6 = 0
Quickly find the sum (2+(−3)=−1) and product (2×−3=−6). Since the coefficient of x is the negative of the sum, it becomes −(−1)x=+x.
Roots of the quadratic equation are given as alpha = 2 and beta = -3.
x2−(α+β)x+αβ=0
Quickly find the sum (2+(−3)=−1) and product (2×−3=−6). Since the coefficient of x is the negative of the sum, it becomes −(−1)x=+x.
Students often forget to invert the sign of the sum of the roots when writing the equation, mistakenly selecting the option with −x instead of +x.
Identify the Roots
Let the given roots be α=2 and β=−3.
α=2,β=−3
Calculate Sum and Product of Roots
Find the sum and product of these roots to substitute into the standard quadratic equation template.
Sum=2+(−3)=−1,Product=2×(−3)=−6
Form the Quadratic Equation
Substitute the calculated sum and product into the standard equation formula: x2−(Sum)x+Product=0.
x2−(−1)x+(−6)=0⟹x2+x−6=0
B is correct because the quadratic equation formed with roots 2 and -3 evaluates to x2+x−6=0.
Mastering the relationship between roots and coefficients allows you to quickly find unknowns in polynomial equations and symmetric functions of roots.
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