Answer:
Step-by-step explanation:
#22
Given
- Equation x² -4x + 1 = k(x - 4) with equal roots
To find
Solution
The equation in standard form is:
- x² -4x + 1 = k(x - 4)
- x² - 4x - kx + 1 + 4 = 0
- x² - (k + 4)x + 5 = 0
When the quadratic equation has equal roots its discriminant is zero
- D = 0
- b² - 4ac = 0
- (k + 4)² - 4*5 = 0
- (k + 4)² = 20
- k + 4 = ± √20
- k = - 4 ± √20
- or
- k = -4 ± 2√5
