1 of 8 0-day streak

Construct a rational quadratic from a surd root

Question 1 of 8

No calculator

One root of a quadratic with rational coefficients is given

\alpha=-4 - \sqrt{3}

The leading coefficient is \(-1\)

(a)3 marks

Complete the exact root pair and use it to obtain the requested coefficients

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(-4 - \sqrt{3}\right)\right)\left(x-\left(-4 - \sqrt{3}\right)\right)

\left(x-\left(-4 - \sqrt{3}\right)\right)\left(x-\left(-4 + \sqrt{3}\right)\right)

-\left(x+\left(-4 - \sqrt{3}\right)\right)\left(x+\left(-4 + \sqrt{3}\right)\right)

-\left(x-\left(-4 - \sqrt{3}\right)\right)\left(x-\left(-4 + \sqrt{3}\right)\right)

Fill the coefficient triple \((a,b,c)\) of the scaled rule in zero form

\(a\) \(b\) \(c\)