Advertisements
Advertisements
Question
Find the values of k for which the given quadratic equation has real and distinct roots:
`9x^2+3kx+4=0`
Solution
The given equation is `9x^2+3kx+4=0`
∴`D=(3k)^2-4xx9xx4=9k^2-144`
The given equation has real and distinct roots if` D>0`
∴`9k^2-144>0`
⇒`9(k^2-16)>0`
⇒`(k-4)(k+4)>0`
⇒`k<-4 or k>4`
shaalaa.com
Relationship Between Discriminant and Nature of Roots
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Write the discriminant of the following quadratic equations:
x2 + 2x + 4 = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
3x2 - 2x + 2 = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
3x2 - 5x + 2 = 0
`3x^2-243=0`
`2x^2-2sqrt2x+1=0`
`sqrt2x^2+7+5sqrt2=0`
`x+1/x=3,x≠0`
`x^2-2ax+(a^2-b^2)=0`
`x^2+6x-(a^2+2a-8)=0`
`x^2-4ax-b^2+4a^2=0`
