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Find the value of k so that the sum of roots of the quadratic equation
\(\left( {k + 1} \right){x^2} + 2kx + 4 = 0\)is equal to product of roots
Sum of roots
Product of roots
Find one root of the\(\left( {a – b} \right){x^2} + \left( {b – c} \right)x + \left( {c – a} \right) = 0\)
x=1 satisfy the given equation.
If\(a{x^2} + bx + c = 0\)has equal roots then c=
If\(x – \dfrac{1}{{x – 2}} = 2 – \dfrac{1}{{x – 2}}\)then x is equal to
By solving we get x=a but x=2 equation is not define.
The value of k which the roots of equation (xโ1)(xโ5)+k=0 differ by 2 is
and
If one root of \({x^2} – 4x + k – 0\)is 6 then the value of k is
The condition for the roots of equation\({x^2} – lx + m = 0\)to differ by one is
a and b are two numbers such that a+b=6, ab=8. Then, a and b are the roots of the quadratic equation.
If one root of a quadratic equation is\(\dfrac{1}{{\sqrt 4 – \sqrt 3 }}\)then the quadratic equation can be
One root
Other root
The quadratic equation
If sum of the roots of \({x^2} – kx + 6 = 0\)is 2 then the value of k is
Sum of roots
The value of k for which
\({x^2} – 4x + k = 0\)has coincident roots is
The value of p so that\({x^2} + 5px + 16 = 0\)has no real root is
For what value of โaโ will the sum of squares of roots of the equation\({x^2} – \left( {a – 2} \right)x – a – 1 = 0\)have the least value
So, the minimum value of
The nature of roots of equation\({x^2} + 2x\sqrt 3 + 3 = 0\)is
The length of a rectangular plot is 8m more than its width. If the length is reduced by 4m and width increased by 3m, the area remains the same. The dimension of the plot are
A dealer sells an article for Rs75 and gains as much percent and the cost price of the article. What is the cost price of the article?
If \({\left( {x – \dfrac{1}{2}} \right)^2} – {\left( {x – \dfrac{3}{2}} \right)^2} = x + 2\)then x=?
A boat takes 90 min less to travel 36km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10km/hr. the speed of the stream is
If\(\dfrac{{x + 3}}{{x – 2}} – \dfrac{{1 – x}}{x} = \dfrac{{17}}{4}\), then x=?
A cistern can be filled in 9hr but it takes 10 hr due to a leak. In how much time will the leak empty the full water?
The sum of the squares if two positive number is 3341 and the difference of their squares is 891. The two numbers are
On solving equation (1) and (2)
The solution of the equation\({7^{1 + x}} + {7^{1 – x}} = 50\)is
If\({x^2} + 2x + c = 0\)and\({x^2} + 4x – 5 = 0\)have a common root which is greater than the other root of second equation then the value of c is
If x=1 is the common root then
The value of x which satisfy the equation
\(\dfrac{2}{{{x^2}}} – \dfrac{5}{x} + 2 = 0\)are
If x=2 and x=3/7 are roots of the equation\(7{x^2} – kx + 2m = 0\), then (k, m)=
Solving (1) and (2) we get,
The sum of squares of three consecutive positive integers is 50 then the integers are:
Numbers are 3, 4, 5.
The value of k for which\({x^2} – 6x + k = 0\)has coincident roots is
If a, b are the roots of the equation\({x^2} – 3x + 2 = 0\)then the equation whose roots are (a+1) and (b+1) is
Id a, b are the roots of the equation\({x^2} – 8x + p = 0\)and\({a^2} + {b^2} = 40\), then p is equal to
A shopkeeper buys a number of books of Rs80. If he had bought 4 more books for the same amount it would have cost Rs1 less. How many books did he buy?
On solving x=16
One root of the equation\(a{x^2} + bx + c = 0\)is square of the other if
If one root of the quadratic equation is\(\sqrt 3 + 1\)then the equation whose coefficient are rational is
The other root will be
So, equation is
If the ratio of the roots of the equation\({x^2} – 2ax + b = 0\)is equal to that of the roots
\({x^2} – 2cx + d = 0\)then
Let the roots be a, b, ka, kb then
From (5) and (6),
The hypotenuse of a grassy land in the shape of a right triangle is 1 meter more than twice the shortest side. If the third side is 7meter more than the shortest side. Find the sides of the grassy land
Hypotenuse
Third side
If the sum of n successive odd natural numbers staring from 3 is 48. Find the number of terms.
If sin q and cos q are the roots of equation\(a{x^2} + bx + c = 0\), then
, here