Advertisements
Advertisements
प्रश्न
Form the quadratic equation if the roots are 3 and 8.
उत्तर
Let α= 3 and β = 8
Sum of roots = α + β
= 3 + 8
= 11
Products of the roots = α x β
= 3 x 8
= 24
Quadratic equation is given by
x2 - (α + β) x + αβ = 0
∴ x2 - 11x + 24 = 0 is the required quadratic equation.
APPEARS IN
संबंधित प्रश्न
Solve : 7y = -3y2 - 4
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`
Form the quadratic equation if its roots are 5 and 7.
Write the roots of following quadratic equation.
(p – 5) (p + 3) = 0
Roots of a quadratic equation are 5 and – 4, then form the quadratic equation
Solve the following quadratic equation.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
Solve the following quadratic equations by formula method.
`y^2 + 1/3y` = 2
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`
Solve the following quadratic equation using formula:
x2 + 10x + 2 = 0
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.
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.
Is (x – 5) a factor of the polynomial x3 – 5x – 30?
One of the roots of equation x2 + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.
Since, `square` is a root of equation x2 + 5x + a = 0
∴ Put x = `square` in the equation
⇒ `square^2 + 5 xx square + a` = 0
⇒ `square + square + a` = 0
⇒ `square + a` = 0
⇒ a = `square`
