Advertisements
Advertisements
Question
If the roots of a quadratic equation are 4 and – 5, then form the quadratic equation
Solution
Let α = 4 and β = – 5
α + β = 4 – 5 = – 1
and α × β = 4 × (– 5) = – 20
∴ The required quadratic equation is
x2 – (α + β)x + αβ = 0
∴ x2 – (– 1) x + (– 20) = 0
∴ x2 + x – 20 = 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?
Solve the quadratic equation : 3x4 - 13x2 +10 = 0.
Choose the correct alternative answer for the following sub-questions and write the correct alphabet.
Which of the following quadratic equation has roots – 3 and – 5?
To decide whether 1 is a root of quadratic equation x2 + 4x – 5 = 0 or not, complete the following activity.
Activity: When x = (______)
L.H.S. = 12 + 4(______) – 5
= 1 + 4 – 5
= (______) – 5
= ______
= R.H.S
Therefore x = 1 is a root of quadratic equation x2 + 4x – 5 = 0
If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’
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.
5m2 – 4m – 2 = 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`
The value of the discriminant of the equation x2 + 6x – 15 = 0 is ______.
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
Is (x – 5) a factor of the polynomial x3 – 5x – 30?
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
