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: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 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
4 - 11 x = 3x2
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Which of the following equations has 2 as a root?
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4, b = ______, c = 3
b2 – 4ac = (–5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
(x2 + 1)2 – x2 = 0 has:
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
