If one root is common between two quadratic e...
If one root is common between two quadratic equations, x2 + 4x + 6 and ax2 + bx+ c, then find the product of the roots of ax2 + bx+ c. (Given: a, b and c are natural numbers.)
• a)
4
• b)
3
• c)
-2
• d)
6
If one root is common between two quadratic equations, x2 + 4x + 6 and...
Solution: Discriminant of (x2 + 4x + 6) < 0 The equation will not have real roots. i.e., x2 + 4x + 6 has complex roots and they are conjugates of each other. One of the roots is also a root of ax2 + bx + c. Conjugate roots always occur in pairs.
So, the product of the roots of (ax2 + bx + c) is same as that of (x2 + 4x + 6). v a = 1 , b = 4 and c = 6 The product = c/a = 6 Hence, option 4.
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If one root is common between two quadratic equations, x2 + 4x + 6 and ax2 + bx+ c, then find the product of the roots of ax2 + bx+ c. (Given: a, b and c are natural numbers.)a)4b)3c)-2d)6Correct answer is option 'D'. Can you explain this answer?
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