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The roots of \(\sqrt 2 {x^6} + 7x + 5\sqrt 2 = 0\)is
The two consecutive positive integer’s sum of whose square is 365 are?
Let consecutive integers be x,x+1
Since, integers are positive so, x=13 two consecutive integers are 13, 14.
The value of k for \(2{x^2} + kx + 3 = 0\)so that they have two equal roots is?
For equal roots, D=0
The roots of the quadratic equation \(9{x^2} – 16 = 0\)are?
The roots of the quadratic equation \({(x + 5)^2} – 36 = 0\)
The roots of the quadratic equation \(\dfrac{{x – 1}}{{x – 2}} + \dfrac{{x – 3}}{{x – 4}} = \dfrac{{10}}{3}(x \ne 2,4)\)are?
The value of P for which \(p{x^2} + 4x + 1 = 0\)has equal roots are?
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The values of p for which \(5p{x^2} – 8x + 2 = 0\)have real roots are?
Divide 12 into two parts such that their product is 32. The two parts are?
Let one part be x, other part=12x
According to the question
The sum of a number and its reciprocal is \(\dfrac{{10}}{3}\).The numbers are?
The product of Raj’s age 5 years ago and his age nine years later is 15. The present age of Raj is?
Raj’s present age is 6 years
The two consecutive odd natural numbers, the sum of whole square is 202 are?
Let consecutive odd numbers is x, x+2
Consecutive numbers is 9, 9+2=11
The difference of the square of two numbers is 45. The square of the smaller number is 4 times the longer number. The numbers are?
Let one number be x
Other number
According to the question
Numbers are 9 and
If \(\dfrac{1}{2}\)is a root of the equation \({x^2} + kx – \dfrac{5}{4} = 0\), the value of k is?
The value of \(\sqrt {6 + \sqrt {6 + \sqrt 2 ….} } \)is?
Let be x
Since x cannot be negative as negative square root is not possible.
So, x=3
If the equation \({x^2} + 4x + k = 0\)has real and distinct roots then?
If the equation \(9{x^2} + 6kx + 4 = 0\)has equal roots then the roots are both equal to?
Roots are equal
D=0
Roots
If \(a{x^2} + bx + c = 0\)has equal roots then c is?
Roots are equal
D=0
The value of k for which the equation \({x^2} + kx + 64 = 0\)and \({x^2} – 8x + k = 0\)will both have real roots is?
In the equation
In the second equation
From 1 and 2
The roots of \(a{x^2} + bx + c = 0,a \ne 0\)are real and unequal, if \({b^2} – 4ac\)is?
Roots are real and unequal if
If 2 is a root of the equation \({x^2} + bx + 12 = 0\)and the equation \({x^2} + bx + q = 0\)has equal roots, then q is equal to?
the equation becomes
it has equal roots
so,
If one root of the equation \(a(b – c){x^2} + b(c – a)x + c(a – b) = 0\)is 1.then the other root is?
Let be the other root
Product of roots is
If the roots of the equation \((a – b){x^2} + (b – c)x + (c – a) = 0\)are equal then?
D=0
If one root of \(2{x^2} + ax + 32 = 0\)is twice the other root then the value of a is?
Let one root be , other be
For what value of a, the roots of the equation\(2{x^2} + 6x + a = 0\). Satisfy the condition \(\left( {\dfrac{\alpha }{\beta }} \right) + \left( {\dfrac{\beta }{\alpha }} \right) < 2\)where \(\alpha \& \beta \)are the roots of equation.
Roots of the equation \({x^2} + x – (a + 1)(a + 2) = 0\)are?
The roots of the equation \(3\sqrt x + 5{(x)^{\dfrac{{ – 1}}{2}}} = \sqrt 2 \)can be found by solving?
Squaring both sides
Two numbers whose sum is 12 and the absolute value of whose difference is 4 are the roots of the equation.
Let the two roots be a and b
A+b=12……(1)
ab=4……(2)
on solving,
a=8,b=4
required equation is
The roots of the equation \({x^{2/3}} + {x^{1/3}} – 2 = 0\)are?
Let
In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles he had in the shop was?
Let the number of bangles be x
=total number of bangles
So,
Total number of bangles is