Question

6. Using the discriminant, determine the value of k that will give 1 solution (i.e. discriminant equals zero) y = kx²-4x + 4 ​

Answer 1

k = 1

Explanation:

Discriminant

`b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0`

`\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}`

`\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}`

`\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}`

As we need to determine the value of k that will give one solution, set the discriminant to zero.

Given equation:

`y=kx^2-4x+4`

Therefore:

• a = k
• b = -4
• c = 4

Substitute these values into the discriminant and solve for k:

`\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}`