Advertisements
Advertisements
प्रश्न
Find the value of a for which the equation `(α-12)x^2+2(α-12)x+2=0` has equal roots.
उत्तर
Given:
`(α-12)x^2+2(α-12)x+2=0 `
Here,
`a=(α=12),b=2(α-12) and c=2`
It is given that the roots of the equation are equal; therefore, we have
`D=0`
⇒`(b^2-4ac)=0`
⇒`{2(α-12)}^2-4xx(α-12)xx2=0`
⇒`4(α^2-24α+144)-8a+96=0`
⇒`4α^2-96α+576-8α+96=0`
⇒`4α^2-104α+672=0`
⇒`α^2-26α+168=0`
⇒`α^2-14α-12α+168=0`
⇒`α(α-14)-12(α-14)=0`
⇒`(α-14)(α-12)=0`
∴`α=14 or α=12`
If the value ofα is 12, the given equation becomes non-quadratic.
Therefore, the value of α will be 14 for the equation to have equal roots.
APPEARS IN
संबंधित प्रश्न
Write the discriminant of the following quadratic equations:
3x2 + 2x + k = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
x2 - 2x + 1 = 0
`4x^2+5x=0`
`x^2-4x-1=0`
`sqrt3x^2+10x-8sqrt3=0`
`3x^2-2sqrt6x+2=0`
`x^2-(sqrt3+1)x+sqrt3=0`
`x^2+5x-(a^+a-6)=0`
`4x^2-4bx-(a^2-b^2)=0`
If the roots of the quadratic equation `(c^2-ab)x^2-2(a^2-bc)x+(b^2-ac)=0` are real and equal, show that either a=0 or `(a^3+b^3+c^3=3abc)`
