If the roots of a quadratic equation are 20 and -7, then find the equation?
Correct answer: C. x2 - 13x - 140 = 0
- A. x2 + 13x - 140 = 0
- B. x2 - 13x + 140 = 0
- C. x2 - 13x - 140 = 0
- D. x2 + 13x + 140 = 0
Explanation
A monic quadratic with roots 20 and -7 is (x - 20)(x + 7) = 0. Expanding gives x² - 13x - 140 = 0, since the sum of roots is 13 and the product is -140. The likely mistake is choosing b, which gives the wrong signs for both the sum and product.
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Quadratic equations contain a squared variable and can be solved by factorisation, completing the square, the quadratic formula, or graphical reasoning. Questions cover roots, the discriminant, and the relationship between roots and coefficients, while distinguishing real and repeated roots from complex or non-real roots.
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