Advertisements
Advertisements
Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
Solution
The equation 3x2 – 4x + 1 = 0 has two real and distinct roots.
D = b2 – 4ac
= (–4)2 – 4(3)(1)
= 16 – 12 > 0
Hence, the roots are real and distinct.
APPEARS IN
RELATED QUESTIONS
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
