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If the roots of a quadratic equation are 20 and -7, then find the equation?
- a)x2 + 13x - 140 = 0
- b)x2 - 13x + 140 = 0
- c)x2 - 13x - 140 = 0
- d)x2 + 13x + 140 = 0
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the roots of a quadratic equation are 20 and -7, then find the equa...
Explanation:
Any quadratic equation is of the form
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
Most Upvoted Answer
If the roots of a quadratic equation are 20 and -7, then find the equa...
The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. To find the equation with roots 20 and -7, we can use the fact that the roots of a quadratic equation are the values of x that make the equation equal to zero.
We know that if a number x is a root of the equation, then (x - r) is a factor of the equation, where r is the root. So, in this case, we have the factors (x - 20) and (x + 7) since 20 and -7 are the roots.
To find the equation, we multiply these factors together:
(x - 20)(x + 7) = 0
Expanding this equation gives us:
x^2 + 7x - 20x - 140 = 0
Combining like terms, we get:
x^2 - 13x - 140 = 0
This is the equation that corresponds to the given roots of 20 and -7. Therefore, the correct answer is option C: x^2 - 13x - 140 = 0.
We know that if a number x is a root of the equation, then (x - r) is a factor of the equation, where r is the root. So, in this case, we have the factors (x - 20) and (x + 7) since 20 and -7 are the roots.
To find the equation, we multiply these factors together:
(x - 20)(x + 7) = 0
Expanding this equation gives us:
x^2 + 7x - 20x - 140 = 0
Combining like terms, we get:
x^2 - 13x - 140 = 0
This is the equation that corresponds to the given roots of 20 and -7. Therefore, the correct answer is option C: x^2 - 13x - 140 = 0.
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If the roots of a quadratic equation are 20 and -7, then find the equation?a)x2+ 13x - 140 = 0b)x2- 13x + 140 = 0c)x2- 13x - 140 = 0d)x2+ 13x + 140 = 0e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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