Advertisements
Advertisements
Question
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Advertisements
Solution
The given quadratic equation is
2x² – px + 4 = 0
one root = 2
Let the other root be a
The sum of the roots 2 + a = `(-(-p))/(2) = p/(2)`
a = `p/(2) - 2` ...(i)
The product of the roots
a x 2 = `(4)/(2) = 2`
⇒ a = 1
Now 2 + a = `p/(2)`
⇒ 2 + 1 = `p/(2)`
⇒ p = 6.
RELATED QUESTIONS
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
Prove that both the roots of the equation (x – a)(x – b) + (x – b)(x – c) + (x – c)(x – a) = 0 are real but they are equal only when a = b = c.
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
15x2 - 28 = x
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
