Question

The equation 2x^2 + x - 1 = 0 has two solutions. Find an equation of the form ax^2 + bx + c = 0, which solutions....

a) are by 5 larger
b) 3 time as large
Can someone please help me with this task? Thank you for your answers!

Answer 1

Explanation:

Let the solution to

2x^2 + x -1 =0

x^2+ (1/2)x -(1/2)

are a and b

Hence a + b = -(1/2) ( minus the coefficient of x )

ab = -1/2 (the constant)

A. We want to have an equation where the roots are a +5 and b+5.

Therefore the sum of the roots is (a+5) + (b+5) = a+ b +10 =(-1/2) + 10 =19/2.

The product is (a+5)(b+5) =ab + 5(a+b) + 25 = (-1/2) + 5(-1/2) + 25 = 22.

So the equation is

x^2-(19/2)x + 22 =0

2x^2-19x + 44 =0

B. We want the roots to be 3a and 3b.

Hence (3a) + (3b) = 3(a+b) = 3(-1/2) =-3/2 and

(3a)(3b) = 9(ab) =9(-1/2)=-9/2.

So the equation is

x^2 +(3/2) x -9/2 = 0

2x^2 + 3x -9 =0.