Advertisements
Advertisements
Question
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.
Options
4
3
5
2
Advertisements
Solution
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to 4.
Explanation:
x = 3 is a root of the equation
x2 – px + 3 = 0 ...(i)
Then x = 3 will satisfy equation (i)
∴ (3)2 – 3p + 3 = 0
9 – 3p + 3 = 0
3p = 12
`\implies` p = `12/3` = 4
RELATED QUESTIONS
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
(x2 + 1)2 – x2 = 0 has ______.
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
