find the value of 'k' for which the quadratic equation is x^2 -2kx +7k-12=0
URGENT!!
Answers
Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "k2" was replaced by "k^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring k2-7k+12
The first term is, k2 its coefficient is 1 .
The middle term is, -7k its coefficient is -7 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 1 • 12 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is -7 .
-12 + -1 = -13
-6 + -2 = -8
-4 + -3 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -3
k2 - 4k - 3k - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
k • (k-4)
Add up the last 2 terms, pulling out common factors :
3 • (k-4)
Step-5 : Add up the four terms of step 4 :
(k-3) • (k-4)
Which is the desired factorization
Equation at the end of step
1
:
(k - 3) • (k - 4) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : k-3 = 0
Add 3 to both sides of the equation :
k = 3
Solving a Single Variable Equation:
2.3 Solve : k-4 = 0
Add 4 to both sides of the equation :
k = 4
Supplement : Solving Quadratic Equation Directly
Solving k2-7k+12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula