Advertisements
Advertisements
प्रश्न
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
Advertisements
उत्तर
Given equation is, `x^2 + 9sqrt(3)x + 24 = 0`
Comparing the given equation with ax2 + bx + c = 0, we get
a = 1, b = `9sqrt(3)`, c = 24
Discriminant, D = b2 – 4ac
= `(9sqrt(3))^2 - 4(1)(24)`
= 243 – 96
= 147
Here, D > 0.
As a result, the roots of the quadratic equation are both real and unequal.
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Find the values of k for which the roots are real and equal in the following quadratic equation:
4x2 – 2(k + 1)x + (k + 4) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 0 `
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
(x2 + 1)2 – x2 = 0 has:
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
Let α and β be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = αn + βn, n = 1, 2, 3, ....., then ______.
