Advertisements
Advertisements
प्रश्न
If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²
उत्तर
x²- 2x - 7= 0
Here, a = 1, b = -2, c = -7
`α + β = (−b)/a =(-(-2))/1 = 2`
`α β =c/a=(-7)/1 =7`
α² + β ² = (α + β)²-2 αβ
=(2)² -2 × (-7)
= 4 + 14
= 18
APPEARS IN
संबंधित प्रश्न
If the roots of 2x2 - 6x + k = 0 are real and equal, find k.
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`
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’
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.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
Solve the following quadratic equations by formula method.
`y^2 + 1/3y` = 2
Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`
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.
Solve the following quadratic equation using formula:
x2 + 10x + 2 = 0
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.
