Advertisements
Advertisements
प्रश्न
Without solving comment upon the nature of roots of each of the following equations:
`"x"^2 – "ax" – "b"^2 = 0`
उत्तर
`"x"^2 – "ax" – "b"^2 = 0`
`"a" = 1, "b" = − "a" and "c" = −"b"^2`
∴ `"Discriminant" = "b"^2 – 4"ac"`
`= (−"a")^2 – 4(1) (−"b")2`
=` "a"^2 + 4"b"^2 =` a positive value
Since `"a"^2 + 4"b"^2` is not a perfect square, roots are irrational
Since D >0, then equation has two real and unequal roots.
APPEARS IN
संबंधित प्रश्न
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John had x marbles.
Without solving, comment upon the nature of roots of the following equations
7x2 – 9x +2 =0
Solve the following equation and give your answer correct to 3 significant figures: 5x² – 3x – 4 = 0
A takes 6 days less than the time taken by B to finish a piece of work. If both A and B work together they can finish in 4 days. Find the time taken by B to finish the work.
Find which of the following equations are quadratic:
7x3 – 2x2 + 10 = (2x – 5)2
Find the quadratic equation, whose solution set is:
{3,5}
For what values of k does the quadratic equation 4x2 − 12x − k = 0 has no real roots?
Check whether the following are quadratic equations: `(x - 3)^3 + 5 = x^3 + 7x^2 - 1`
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
Which of the following is not a quadratic equation?
If x2 – 4x = 5, the value of x is ______.
