Advertisements
Advertisements
Question
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Solution
Given quadratic equation is: 4x2 – 5x – 1 = 0
Comparing the above equation with ax2 + bx + c = 0,
We get a = 4, b = –5 and c = –1
Now, b2 – 4ac = (–5)2 – 4(4)(–1)
= 25 + 16
= 41 > 0
Hence, roots of the quadratic equation are real and distinct.
APPEARS IN
RELATED QUESTIONS
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
Find the value of 'p' for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
