Advertisements
Advertisements
प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Advertisements
उत्तर
3x2 + 2x - 1 = 0
Here, a = 3, b = 2 and c = -1
D = b2 - 4ac
= 4 - 4 x 3 x (-1)
⇒ D = 4 + 12
= 16 > 0.
संबंधित प्रश्न
If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.
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 ?
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Which of the following equations has the sum of its roots as 3?
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
