Advertisements
Advertisements
Question
Solve using formula.
y2 + `1/3`y = 2.
Solution
y2 + `1/3`y = 2
Multiplying both sides by 3,
∴ 3y2 + y = 6
∴ 3y2 + y − 6 = 0
Comparing the above equation with ay2 + by + c = 0, we get,
a = 3, b = 1, c = −6
∴ b2 – 4ac = (1)2 – 4 × 3 × (−6) = 1 + 72 = 73.
`y = (-b +- sqrt(b^2 - 4ac))/(2a)`
`y = (-1 +- sqrt(73))/(2 × 3)`
`y = (-1 +- sqrt(73))/(6)`
`y = (-1 + sqrt(73))/(6) "or" y = (-1 - sqrt(73))/(6)`
∴ The roots of the given quadratic equation are `(-1 + sqrt(73))/(6) "and" (-1 - sqrt(73))/(6)`.
APPEARS IN
RELATED QUESTIONS
Compare the given quadratic equation to the general form and write values of a, b, c.
x2 – 7x + 5 = 0
Compare the given quadratic equation to the general form and write values of a,b, c.
2m2 = 5m – 5
Solve using formula.
x2 + 6x + 5 = 0
Solve using formula.
x2 – 3x – 2 = 0
Solve using formula.
3m2 + 2m – 7 = 0
Solve using formula.
5x2 + 13x + 8 = 0
The roots of the following quadratic equation is real and equal, find k.
kx (x – 2) + 6 = 0
Find the value of discriminant of the following equation.
2y2 − y + 2 = 0
Find the value of discriminant of the following equation.
\[\sqrt{5} x^2 - x - \sqrt{5} = 0\]
One of the roots of quadratic equation \[2 x^2 + kx - 2 = 0\] is –2. find k.
Two roots of quadratic equation is given ; frame the equation.
\[1 - 3\sqrt{5} \text{ and } 1 + 3\sqrt{5}\]
Determine the nature of root of the quadratic equation.
\[3 x^2 - 5x + 7 = 0\]
Determine the nature of root of the quadratic equation.
\[\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0\]
Determine the nature of root of the quadratic equation.
m2 - 2m + 1 = 0
The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.
Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation \[2 x^2 + 2\left( p + q \right)x + p^2 + q^2 = 0\]
The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.
If 2 and 5 are the roots of the quadratic equation, then complete the following activity to form quadratic equation:
Activity:
Let α = 2 and β = 5 are the roots of the quadratic equation.
Then quadratic equation is:
x2 − (α + β)x + αβ = 0
∴ `x^2 - (2 + square)x + square xx 5 = 0`
∴ `x^2 - square x + square = 0`
