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PSLE Foundation Mathematics

<p>The roots of the quadratic equation $x^2+4x-1=0$ are $\alpha$ and $\beta$.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Write down the values of $\alpha+\beta$ and of $\alpha\beta$.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Without solving the equation, find the value of each of the following.</div><ol class="i-list"><li data-list-item-id="item-b-i" data-list-item-path="item-b/item-b-i"><div class="list-item-paragraph">$\dfrac{1}{\alpha^2}+\dfrac{1}{\beta^2}$</div></li><li data-list-item-id="item-b-ii" data-list-item-path="item-b/item-b-ii"><div class="list-item-paragraph">$\left(\alpha-\dfrac{2}{\beta^2}\right)\left(\beta-\dfrac{2}{\alpha^2}\right)$</div></li></ol></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Determine the quadratic equation with integer coefficients which has roots $\alpha-\dfrac{2}{\beta^2}$ and $\beta-\dfrac{2}{\alpha^2}$.</div></li></ol>

The roots of the quadratic equation $x^2+4x-1=0$ are $\alpha$ and $\beta$.

Write down the values of $\alpha+\beta$ and of $\alpha\beta$.

Without solving the equation, find the value of each of the following.

Determine the quadratic equation with integer coefficients which has roots $\alpha-\dfrac{2}{\beta^2}$ and $\beta-\dfrac{2}{\alpha^2}$.

Sum and Product of Roots

Structured chain to an equation with adjusted roots

Quadratic Functions, Equations and Inequalities

<p>The roots of the equation $2x^4-4x^3-5x^2+6x-10=0$ are $\alpha$, $\beta$, $\gamma$ and $\delta$.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Write down the values of $\sum\alpha$, $\sum\alpha\beta$, $\sum\alpha\beta\gamma$ and $\alpha\beta\gamma\delta$.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Hence find the value of $\alpha^2+\beta^2+\gamma^2+\delta^2$.</div></li></ol>

The roots of the equation $2x^4-4x^3-5x^2+6x-10=0$ are $\alpha$, $\beta$, $\gamma$ and $\delta$.

Root sums and products of a quartic

Polynomials, Cubic Equations and Partial Fractions

<p>If $\alpha $ and $\beta $ are the roots of the equation $3{{x}^{2}}+7x-18=0$ where $\alpha &gt;\beta $, find the value for each of the following. </p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{1}{\alpha }+\frac{1}{\beta }$</div></li><li><div class="list-item-paragraph">${{\alpha }^{2}}+{{\beta }^{2}}$</div></li><li><div class="list-item-paragraph">$\alpha -\beta $</div></li><li><div class="list-item-paragraph">${{\alpha }^{3}}-{{\beta }^{3}}$</div></li><li><div class="list-item-paragraph">${{\alpha }^{4}}+{{\beta }^{4}}$</div></li></ol>

If $\alpha $ and $\beta $ are the roots of the equation $3{{x}^{2}}+7x-18=0$ where $\alpha >\beta $, find the value for each of the following. 

Math Question Bank