Advertisements
Advertisements
Question
Decide whether the following equation is quadratic equation or not.
`"y"^2 + 1/"y" = 2`
Solution
`"y"^2 + 1/"y" = 2`
∴ `"y" xx "y"^2 + "y" xx 1/"y" = "y" xx 2` ....[Multiplying both sides by y]
∴ y3 + 1 = 2y
∴ y3 − 2y + 1 = 0
Here y is the only variable and the maximum index of the variable is not 2.
∴ It is not a quadratic equation.
RELATED QUESTIONS
If one of the roots of the quadratic equation x2 - 11x + k = 0 is 9, then find the value of k
Which of the following is a quadratic equation?
(a)` (x^2+1)=(2-x)^2+3` (b)` x^3-x^2=(x-1)^3`
(c) `2x^+3=(5+x)(2x-3)` (d) None of these
If one root of the equation `2x^2+ax+6=0` 2 then a=?
(a)7 (b)-7 (c) 7/2 (d)-7/2
If one root of the equation` 3x^2-10x+3=0 is 1/3` then the other root is
(a) `-1/3` (b) `1/3` (c)`-3` (d)`3`
If one root of `5x^2+13x+k=0` be the reciprocal of the other root then the value of k is
`(a)0 (b)1 (c)2 (d)5`
The roots of the equation `ax^2+bx+c=0` will be reciprocal each other if
(a)a=b (b)b=c (c)=a (d)= none of these
The sum of two natural numbers is 8 and their product is 15., Find the numbers.
Find the solution of the quadratic equation `3sqrt3x^2+10x+sqrt3=0`
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` write the other zero.
If the roots of the quadratic equation `px(x-2)+=0` are equal, find the value of p
Find the value of k for which the quadratic equation `9x^2-3kx+k=0` has equal roots.
Decide whether the following equation is quadratic equation or not.
m3 + 3m2 – 2 = 3m3
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
Choose the correct answer for the following question.
The roots of x2 + kx + k = 0 are real and equal, find k.
Choose the correct answer for the following question.
Out of the following equations, find the equation having the sum of its roots –5.
Two water taps together can fill a tank in `1(7)/(8)` hours. The tap with 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.
Solve for x : `1/(2a + b + 2x) =1/(2a) + 1/b + 1/(2x); x ≠ 0, x ≠ (−2a −b)/2`, a, b ≠ 0
Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has
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 = ______
