Question

I need help with these questions ( see image for question ).
Please show working.
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Answer 1

• k = -4 ± 2√5

Explanation:

#22

Given

• Equation x² -4x + 1 = k(x - 4) with equal roots

To find

• The value of k

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