Advertisements
Advertisements
Question
Form the quadratic equation if its roots are 5 and 7.
Solution
Roots of a quadratic equation are 5 and 7.
Let α = 5 and β = 7.
α + β = 5 +7 = 12
αβ = 5 × 7 = 35 .
∴ The quadratic equation is given by .
x2 - (α+β ) x + α β = 0
∴ x2 - 12x + 35 = 0
APPEARS IN
RELATED QUESTIONS
Solve : 7y = -3y2 - 4
If the roots of x² + kx + k = 0 are real and equal, what is the value of k?
If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²
If α and β are the roots of the quadratic equation `x^2 - 4x - 6 = 0`, find the values of (i) `α^2+β^2` (ii) `α^3+β^3`
If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.
Solve the quadratic equation : 3x4 - 13x2 +10 = 0.
Convert the following equations into simultaneous equations and solve:
`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
Degree of quadratic equation is always ______
Write the roots of following quadratic equation.
(p – 5) (p + 3) = 0
If the roots of the given quadratic equation are real and equal, then find the value of ‘k’
kx(x – 2) + 6 = 0
Solve the following quadratic equation.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
Solve the following quadratic equation.
`1/(4 - "p") - 1/(2 + "p") = 1/4`
Determine whether 2 is a root of quadratic equation 2m2 – 5m = 0.
One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.
Activity:
One of the roots of equation kx2 – 10x + 3 = 0 is 3.
Putting x = `square` in the above equation
∴ `"k"(square)^2 - 10 xx square + 3` = 0
∴ `square` – 30 + 3 = 0
∴ 9k = `square`
∴ k = `square`
Determine whether (x – 3) is a factor of polynomial x3 – 19x + 30.
Let P(x) = x3 – 19x + 30
By remainder theorem, `square` will be a factor of P(x), if P(3) = 0
Now, P(3) = `square` – 19 `square` + 30
= `square – square` + 30
= `square – square`
= 0
∵ P(3) = 0
Hence, `square` is a factor of polynomial x3 – 19x + 30.
If the sum of the roots of the quadratic equation x2 + kx + 6 = 0 is 6, then the value of k is ______.
If the roots of the quadratic equation x2 + 12x + a = 0 are real and equal, then find the value of a.
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.
