If m and ( m + 4) are the roots of \(4x^2 - 4x -
FURTHER MATHEMATICS
WAEC 2023
If m and ( m + 4) are the roots of \(4x^2 - 4x - 15 = 0\), find the equation whose roots are 2 m and (2 m + 8).
- A. \(x^2+8x-15=0\)
- B. \(x^2-2x-15=0\)
- C. \(x^2-8x-15=0\)
- D. \(x^2+2x+15=0\)
Correct Answer: B. \(x^2-2x-15=0\)
Explanation
\(x^2-\)(sum of roots)\(x+\)(product of roots) = \(0\)
\(4x^2-4x-15=0\)
Divide through by 4
\(=x^2-x-\frac{15}{4}=0\)
\(=x^2-x+(-\frac{15}{4})=0\)
\(=x^2-(1)x+(-\frac{15}{4})=0\)
sum of roots =1
= m + (m + 4) = 1
=2m+4=1
=2m=-3
=m=-\(\frac{3}{2}\)
The equation whose roots are 2m and 2m+8
2m=2×-\(\frac{3}{2}=-3\)and \(2m+8=2×-\frac{3}{2}+8=5\)
\(=x^2-(-3+5)x+(-3)(5)=0\)
\(=x^2-2x+(-15)=0\)
\(∴x^2-2x-15=0\)
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