Advertisements
Advertisements
Question
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
Equation 2x2 – 3x + 1 = 0 has ______.
