$given \: equation \: is \\ 30 {x}^{2} - 5x - 10 \\ taking \: out \: 5 \: which \: is \: common \: gives \\ 5(6 {x}^{2} - x - 2) \\ by \: factorization \: \\ (multiply \: = - 12 \: and \: add \: - 1) \\ 5(6 {x}^{2} + 3x - 4x - 2) \\ 5(3x(2x + 1) - 2(2x + 1)) \\ = 5(2x + 1)(3x - 2) \\ so \: answer \: is \: option \: 5$

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7 0

3 years ago

Form quadratic equation with roots (alpha² + 1/alpha²) and (beta²+1/beta²)

sashaice [31]

Answer:

What equation? Here’s a big tip for you, equations contain an ‘equals sign’ (‘=’) and something that they are equal to. I’m assuming your equation is:

ax2+bx+c=0

I’m going to use p and q for the roots of the equation as they are easier to type than α and β . Thus we have:

a(x−p)(z−q)=0⇒ax2−a(p+q)x+apq=0

Equating coefficients with our initial equation:

x1 : b=−a(p+q)⇒p+q=−ba

x0 : c=apq⇒pq=ca

Now p2+q2=p2+2pq+q2−2pq=(p+q)2−2pq

=(−ba)2−2ca

=b2a2−2ca

=b2−2aca2

3 0

3 years ago