Advertisements
Advertisements
प्रश्न
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
उत्तर
`3"x"^2 – 12"x" + (n – 5) = 0`
Here a = 3, b = − 12 and c = n – 5
Given: equation has equal roots
Then D = 0
⟹ `"b"^2 – 4"ac" = 0`
⟹ `[− 12]^2 – 4(3)("n" – 5) = 0`
⟹ 144 – 12n + 60 = 0
⟹ − 12n = − 204
⟹ `"n"=(-204)/-12=17`
APPEARS IN
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Solve for x : ` 2x^2+6sqrt3x-60=0`
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
