Advertisements
Advertisements
प्रश्न
In the equation `ax^2+bx+c=0` it is given that `D=(b^2-4ac)>0`
equation are
(a) real and equal (b) real and unequal (c) imaginary (d) none of these
उत्तर
We know that when discriminant, D > 0, the roots of the given quadratic equation are real and unequal.
APPEARS IN
संबंधित प्रश्न
If x=3 is a solution of the equation `3x^2+(k-1)x+9=0` then k=?
(a) 11 (b)-11 (c)13 (d)-13
The roots of the quadratic equation `2x^2-x-6=0`
(a)`-2, 3/2` (b) `2, -3/2`
(c)` -2, 3/2` (d) `2, 3/2`
Show the x= -3 is a solution of `x^2+6x+9=0`
If the roots of the quadratic equation `2x^2+8x+k=0` are equal then find the value of k.
If the quadratic equation `px^2-2sqrt5px+15=0` has two equal roots then find the value of p.
Solve for x: `3x^2-2sqrt6x+2=0`
Write the following equation in the form ax2 + bx + c = 0, then write the values of a, b, c for the equation.
(x – 1)2 = 2x + 3
If in an A. P., d = 10, find t6 - t2.
Two water taps together can fill a tank in `1 7/8` hours. The tap with a longer diameter takes 2 hours less than the tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
In the adjoining fig. `square` ABCD is a trapezium AB || CD and its area is 33 cm2. From the information given in the figure find the lengths of all sides of the `square` ABCD. Fill in the empty boxes to get the solution.
Solution: `square` ABCD is a trapezium.
AB || CD
`"A"(square "ABCD") = 1/2 ("AB" + "CD") xx`______
33 = `1/2 ("x" + 2"x" + 1) xx `______
∴ ______ = (3x + 1) × ______
∴ 3x2 +______ − ______ = 0
∴ 3x(______) + 10(______) = 0
∴ (3x + 10) (______) = 0
∴ (3x + 10) = 0 or ______ = 0
∴ x = `-10/3` or x = ______
But length is never negative.
∴ `"x" ≠ -10/3`
∴ x = ______
AB = ______, CD = ______, AD = BC = ______