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Determine parameters in a polynomial identity

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
Expanded quadratic with two parametersExpanded cubic with two parametersNOWMix of allRecommended
Question 1 of 8

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For every real value of \(x\), the expressions below are equal

\[P(x)=-4x^2 + 5x + 7\]
\[Q(x)=-4x^2 - x + px + 2 + q\]

The required identity is \(P(x)=Q(x)\)

For a numerical check, evaluate the displayed expressions at \(x=0\)

(a)1 mark

Which parameter values make the stated equality true for every real input?

Select the coefficient condition that uses the identity correctly

(b)2 marks

Solve the coefficient conditions and enter the values of \(p, q\)

(c)1 mark

Evaluate the displayed polynomial at \(x=0\) and enter \(P(0)\)