Advertisements
Advertisements
प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Advertisements
उत्तर
The given quadratic equation is 3y2 + 7y + 4 = 0.
Comparing the given equation with ax2 + bx + c = 0 we get,
a = 3, b = 7 and c = 4
`y=(-b+-sqrt(b^2-4ac))/(2a)`
`y=(-7+-sqrt(7^2-4ac))/(2(3))`
`y=(-7+-sqrt(49-48))/6`
`y=(-7+-sqrt(1))/6`
`y=(-7+-1)/(6)`
`y=(-7+1)/(6) or y=(-7-1)/(6)`
`y=-6/6=-1 or y=-8/6=-4/3`
`y=-1 or y=-4/3`
Therefore `-1` and `-4/3` are the roots of given equation.
APPEARS IN
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
Find the values of k for which the roots are real and equal in the following equation:
2x2 + kx + 3 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
If the equation \[\left(1 + m^2 \right) x^2 + 2mcx + \left(c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Solve the following quadratic equation using formula method only :
x2 +10x- 8= 0
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
`(2)/x^2 - (5)/x + 2` = 0
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
Find the sum of the roots of the equation x2 – 8x + 2 = 0
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
