Given a quadratic equation, find a value of a such that the quadratic equation would have one root less than -1 and another greater than 1.

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Roy Brady · Accepted Answer

Step 1It means this polynomial has two real roots and that 1 separates the roots.The discriminantΔ=(2a−3)2−4(a2+a+1)(a−5)&amp;gt;0Under this hypothesis, there is a high-school theorem on the separation of roots:Here, the leading coefficient is a2+a+1, which is always positive (its roots are the complex cubic roots of unity). So the separating condition is merelyp(1)=a2+a+1+2a−3+a−5=a2+4a−7&amp;lt;0.Note that if p(1)&amp;lt;0, the quadratic polynomial necessarily has tow real roots;, so the first condition is automatically satisfied.

zevillageobau · Accepted Answer

Step 1The hint.Let f(x)=(a2+a+1)x2+(2a−3)x+a−5.Thus, sincea2+a+1=(a+12)2+34&amp;gt;0,we need to solve the following inequality:f(1)&amp;lt;0

Given a quadratic equation, find a value of

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