Advertisements
Advertisements
Question
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Solution
x2 +3x+1=0
b2 - 4ac
= (3)2 - 4(1)(1)
= 9 - 4
= 5
Since discriminant is positive, hence the roots are real and irrational.
APPEARS IN
RELATED QUESTIONS
Determine the nature of the roots of the following quadratic equation:
(b + c)x2 - (a + b + c)x + a = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
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 ?
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
