Advertisements
Advertisements
प्रश्न
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
उत्तर
We have, `x^2 + 2sqrt(2)x - 6` = 0
Now, by using the formula x = `(-b +- sqrt(b^2 - 4ac))/(2a)`, we get
x = `(-2sqrt(2) +- sqrt((2sqrt(2))^2 - 4 xx 1 xx (-6)))/(2 xx 1)`
⇒ x = `(-2sqrt(2) +- sqrt(8 + 24))/2`
⇒ x = `(-2sqrt(2) +- 4sqrt(2))/2`
= `- sqrt(2) +- 2sqrt(2)`
⇒ x = `-sqrt(2) + 2sqrt(2)`, x = `-sqrt(2) - 2sqrt(2)`
⇒ x = `sqrt(2)`, x = `-3sqrt(2)`
APPEARS IN
संबंधित प्रश्न
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
The roots of quadratic equation x2 – 1 = 0 are ______.
