The polynomial \(P(x) = 2{x^3} + a{x^2} + bx + 6\) is divisible by \(x-1\) and leaves the remainder of \(-12\) when divided by \(x+2\). The values of \(a\) and \(b\) are?
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Polynomials - Diagnostic Quiz 1
Question 2 of 8
What are the roots of \({x^3} + 5{x^2} + 8x + 4 = 0\)
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Polynomials - Diagnostic Quiz 1
Question 3 of 8
The product of two roots of the polynomial equation \(2{x^3} - k{x^2} - 8x + 4 = 0\) is \(1\). Find the value of \(k\)
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Polynomials - Diagnostic Quiz 1
Question 4 of 8
Give that the equation \({x^3} - 7{x^2} + 16x + k = 0\) has two equal and integral roots, find the value of \(k\).
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Polynomials - Diagnostic Quiz 1
Question 5 of 8
\(P(x) = {x^3} + {x^2} - 5x + 3\) has a root of multiplicity of 2. The roots are
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Polynomials - Diagnostic Quiz 1
Question 6 of 8
Given that \(P(x) = {x^4} + 4{x^3} - 16x + k\) has a root of multiplicity of \(3\) and \(k<0\). Find the value of \(k\).
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Polynomials - Diagnostic Quiz 1
Question 7 of 8
Which of the graphs below is the graph of \(y = x{\left( {x - 2} \right)^2}\,\)?
A
B
C
D
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Polynomials - Diagnostic Quiz 1
Question 8 of 8
Which of the graphs below is the graph of \(y = {(x - 1)^2}{\left( {x + 2} \right)^2}\,\)?
A
B
C
D
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The polynomial \(P(x) = 2{x^3} + a{x^2} + bx + 6\) is divisible by \(x-1\) and leaves the remainder of \(-12\) when divided by \(x+2\). The values of \(a\) and \(b\) are?
Answer Click to reveal
\(a=-3\), \(b=-5\)
Worked SolutionClick to reveal
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