Advertisements
Advertisements
Question
Form the quadratic equation if the roots are 3 and 8.
Solution
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
RELATED QUESTIONS
If the roots of 2x2 - 6x + k = 0 are real and equal, find k.
Solve : 7y = -3y2 - 4
If the roots of x² + kx + k = 0 are real and equal, what is the value of k?
If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.
Form the quadratic equation if its roots are 5 and 7.
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.
Which of the following quadratic equation has roots – 3 and – 5?
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If one of the roots of quadratic equation X2 – kX + 27 = 0 is 3, then find the value of ‘k’
Write the roots of following quadratic equation.
(p – 5) (p + 3) = 0
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 the roots of a quadratic equation are 4 and – 5, then form the quadratic equation
Roots of a quadratic equation are 5 and – 4, then form the quadratic equation
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.
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)`.
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`
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
