Advertisements
Advertisements
Question
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Advertisements
Solution
`"x"^2 + 1/2 "x" = 3`
2x2 + x = 6
2x2 + x - 6 = 0
a = 2 ; b = 1 ; c = -6
D = b2 - 4ac
= (1)2 - 4(2)(-6)
= 1 + 48
= 49
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(-1 +- sqrt 49)/4`
x = `(- 1 + 7)/4` , x = `(- 1 - 7)/4`
x = `6/4` , x = `-8/4`
x = `3/2` , x = - 2
APPEARS IN
RELATED QUESTIONS
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 – 24abcdx + 16c2d2 = 0, a ≠ 0, b ≠ 0
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
x2 + 4x + 5 = 0
From the quadratic equation if the roots are 6 and 7.
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, the value of k is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
