1 of 8 0-day streak

Construct a rational quadratic from a surd root

Question 1 of 8

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One root of a quadratic with rational coefficients is given

\alpha=-1 - \sqrt{17}

The leading coefficient is \(1\)

(a)3 marks

Construct the quadratic from the given root, keeping the leading coefficient shown

Enter the rational part, surd coefficient and radicand of the other root

Rational part Surd coefficient Radicand

(b)1 mark

Which factor product uses the two roots and the stated leading coefficient?

\left(x-\left(-1 - \sqrt{17}\right)\right)\left(x-\left(1 - \sqrt{17}\right)\right)

\left(x+\left(-1 - \sqrt{17}\right)\right)\left(x+\left(-1 + \sqrt{17}\right)\right)

\left(x-\left(-1 - \sqrt{17}\right)\right)\left(x-\left(-1 + \sqrt{17}\right)\right)

\left(x-\left(-1 - \sqrt{17}\right)\right)\left(x-\left(-1 - \sqrt{17}\right)\right)

Fill the coefficients of the monic rule in the form \(x^2+bx+c=0\)

\(b\) \(c\)