α and β are the roots of the equation 2x^2 -5x + c =0. If 4α -2β = 7, find the value of c

Answer 1

The sum of the roots is -B/A

2x²-5x+C=0

A=2

B=-5

Sum of α and β = -(-5)/2= 5/2

α + β = 5/2

Multiply both sides by 2

2α +2β = 5

4α -2β = 7

Elimination gives

6α=12

α=2

Substitution

2(2) +2β = 5

4+2β = 5

2β = 1

β = 1/2

The factors of the quadratic would need to be

(2x-1)(x-2)=0

Foil that

2x²-5x+2=0

C=2