Advertisements
Advertisements
प्रश्न
Solve the following equation by using formula :
x2 + (4 – 3a)x – 12a = 0
उत्तर
x2 + (4 – 3a)x – 12a = 0
Here a = 1, b = 4 – 3a, c = -12a
∴ D = b2 – 4ac
= (4 – 3a)2 – 4 x 1 x (–12a)
= 16 – 24a + 9a2 + 48a
= 16 + 24a + 9a2 = (4 + 3a)
∴ x = `(-b ± sqrt("D"))/(2a)`
= `(-(4 - 3a) ± sqrt(4 + 3a^2))/(2 xx 1)`
= `(3a - 4 ± 3a + 4)/(2)`
∴ x1 = `(3a - 4 + 3a + 4)/(2)`
= `(6a)/(2)`
= 3a
and
x2 = `(3a - 4 - 3a - 4)/(2)`
= `(-8)/(2)`
= –4
∴ Roots are 3a, –4.
APPEARS IN
संबंधित प्रश्न
Represent the following situation in the form of a quadratic equation:
Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.
In the following, determine whether the given values are solutions of the given equation or not:
`x^2 - 3sqrt3x+6=0`, `x=sqrt3`, `x=-2sqrt3`
In the following, find the value of k for which the given value is a solution of the given equation:
x2 + 3ax + k = 0, x = -a
Solve the following equation using the formula:
`(2x)/(x - 4) + (2x - 5)/(x - 3) = 8 1/3`
Which of the following are quadratic equation in x?
`2x^2+5/2xsqrt3=0`
`x^2+5x-(a^2+a-6)=0`
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3,x≠2,4`
`3((3x-1)/(2x+3))-2((2x+3)/(3x-1))=5,x≠1/3,-3/2`
For what values of k does the quadratic equation 4x2 − 12x − k = 0 has no real roots?
If `(2)/(3)` is a solution of the equation 7x2 + kx – 3 = 0, find the value of k.
