Question

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.

Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
Substitution: x = StartFraction negative 5 plus or minus StartRoot 5 squared minus 4(2)(negative 3) EndRoot Over 2(negative 2) EndFraction
What error did Zacharias make?

Answer 1

The solution of the given equation is

`x = (3)/(2) , 1`

Step-by-step explanation:

Step-by-step explanation:-

Given equation is - 2 x² + 5 x - 3 = 0

By using quadratic formula

`x = \frac{-b-\sqrt{b^(2) - 4 a c} }{2 a} , x = \frac{-b+\sqrt{b^(2) - 4 a c} }{2 a}`

Given equation a = -2 , b = 5 ,c = -3

`x = \frac{-5-\sqrt{(5)^(2) - 4 (-2) (-3)} }{2 (-2)} , x = \frac{-5+\sqrt{(5)^(2) - 4 (-2) (-3)} }{2 (-2)}`

`x = (-5-√(1) )/(-4) = (-6)/(-4) = (3)/(2)`

and

`x = (-5+√(1) )/(-4) = (-5+1)/(-4) = (-4)/(-4)=1`

The solution of the given equation is

`x = (3)/(2) , 1`