Home > Algebra > Comparing Methods for Solving Quadratics

One solution of #kx^2- 5x +k=0# is 3. How do you find the other solution?

Answer 1

Genesis Allen

Other solution is #x=1/3#

As one solution of #kx^2-5x+k=0# is #3#, we have

#kxx3^2-5xx3+k=0#

or #9k-15+k=0#

or #10k=15# i.e. #k=1.5#

Hence equation is #1.5x^2-5x+1.5=0#

or #3x^2-10x+3=0#

or #3x^2-9x-x+3=0#

or #(3x(x-3)-1(x-3)=0#

or #(3x-1)(x-3)=0#

#:.# either #3x-1=0# i.e. #x=1/3#

or #x-3=0# i.e. #x=3#

Hence, other solution is #x=1/3#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Alexander

To find the other solution, use the fact that the sum of the solutions of a quadratic equation ( ax^2 + bx + c = 0 ) is equal to (-\frac{b}{a}). If one solution is 3, substitute (x = 3) into the equation and solve for (k). Then use the value of (k) to find the other solution.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.