Solve for x in the equation 5^2x-6×5^x+5=0?

 Given that 5^2x-6×5^x+5=0

Put 5^x=t - - - - - - - - - -- -- - - -:- (1), so we get,

t²-6t+5=0 , which is quadratic equation in t.

=> t²-t-5t+5=0  => (t²-t)-(5t-5)=0

=> t(t-1)-5(t-1)=0 => (t-1)(t-5)=0

=> Either t-1=0 or t-5=0

=> t=1 or t=5 

=> t=1, 5

Case1:- When t=1, then 5^x=1  [By using (1)]

=> 5^x=5^0 => x=0

Case2:- When t=5

=> 5^x=5  => 5^x=5^1

=> x=1

From case1 and case2, we get, x=0,1 Ans.

parallelogram law of vector addition.

 

The vectors-2i ̂+4j ̂+4k ̂ and-4i ̂-2k ̂ represent the diagonals BD and AC of a parallelogram ABCD.Then find the area of the Parallelogram. [ISC2006]

 

Find the discriminant of 4√3x²+10x+√3=0

 Given that 4√3x² +10x+√3=0

Comparing the given quadratic equation  with standard quadratic equation  x²+bx+c=0

So a=4√3, b=10 and c=√3

The discriminant D=b²-4ac

=> D=(10)²-4(4√3)(√3)

=> D=100-4(12)

=> D=100-48

=> D=52 Ans.

Define Parallelogram law of vector addition.

 

What is vector product(cross product )?

 

Solve -3 less than 2x-5.

 

If cosθ=1/2, then find the value of tanθ.

Find the value of k, for which 3 is a root of the equation kx²-7x+3=0.

 Since 3 is a root of the quadratic equation kx²-7x+3=0, then k(3)²-7(3)+3=0

=> 9k-21+3=0 => 9k-18=0

=> 9k=18 => k= 2 Ans.

Find a quadratic polynomial, whose sum of zeroes is 5 and porduct of zeroes is 6.

 Let A and B are zeroes of a quadratic polynomial.

Then the required polynomial will be,

x² -(A+B)x+AB

Here A+B=5 and AB=6

Now the required quadratic polynomial is,

x²-5x+6   Ans.