Advertisements
Advertisements
Question
Solve for x: `2x^2 + 7/2 x + 3/4 = 0`.
Sum
Solution
The quadratic equation is of the form:
`ax^2 + bx + c = 0`
x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
Here, a + 2, b = `7/2,` c = `3/4`
Calculate the Discriminant `(b^2 - 4ac)`
`b^2 - 4ac = (7/2)^2 - 4(2) (3/4)`
`b^2 - 4ac = 49/4 - 4 * 2 * 3/4`
`b^2 - 4ac = 49/4 - 24/4`
`b^2 - 4ac = 25/4`
The quadratic formula becomes:
`x = (-b ± sqrt(b^2 - 4ac))/(2a)`
Substitute `b = 7/2, b^2 - 4ac = 25/4, and a = 2`:
`x = (-7/2 ± sqrt(25/4))/(2 xx 2)`
`x = (-7/2 ± 5/2)/4`
Split into two cases for + and −:
Case 1: `x = (-7/2 + 5/2)/4`
= `(- 2)/4`
= `(-1)/2`
Case 2: `x = (-7/2 - 5/2)/4`
`x = (-12/2)/4`
= `(-6)/4`
= `(-3)/2`
`therefore x = (-1)/2 and x = (-3)/2`
shaalaa.com
Is there an error in this question or solution?
