Question

Given f(x)=3x^2+kx+4 and the remainder when f(x) is divided by x-4 is 68 then What is the value of k?

Answer 1

• k = 4

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Given

• Function f(x) = 3x² + kx + 4,
• Remainder of f(x) / (x - 4) is 68.

According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.

• f(x) = 3x² + kx + 4 - 68 = 3x² + kx - 64 = 0

When x = 4

• 3*4² + k*4 - 64 = 0
• 48 + 4k - 64 = 0
• 4k - 16 = 0
• 4k = 16
• k = 4