Question

The quadratic equation 2x^2+bx+18=0 has a double root . Find all values of b

Answer 1

ANSWER


`\boxed {b = \pm12}`

Step-by-step explanation


The given quadratic equation is


`2 {x}^(2) + bx + 18 = 0`

By comparing to


`a {x}^(2) +b x + 18 = 0`


`a=2,c=18`


If this equation has a double root, then the discriminant is zero.

Thus,


`{b}^(2) - 4ac = 0`


We substitute the values into the formula to obtain,



`{b}^(2) - 4(2)(18) = 0`



`\Rightarrow \: {b}^(2) - 144 = 0`




`\Rightarrow \: {b}^(2) = 144`



We take the square root of both sides to obtain,


`b= \pm \: √(144)`



`\Rightarrow \: b= \pm 12`