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adoni [48]
3 years ago
7

Write the quadratic equation whose roots are -1 and -5 , and whose leading coefficient is 2 . (Use the letter to represent the v

ariable.)
Mathematics
1 answer:
geniusboy [140]3 years ago
3 0

Answer:

2x^2+12x+10=0

Step-by-step explanation:

When you have the roots r1, r2 and the leading coefficient a of a quadratic equation, its factorization is

a(x - r1)(x - r2)

and the quadratic equation would be

a(x - r1)(x - r2) = 0

In this case r1 = -1, r2 = -5 and a = 2, so the quadratic equation is

\large 2(x-(-1))(x-(-5))=0\Rightarrow 2(x+1)(x+5)=0\Rightarrow\\\\\Rightarrow2(x^2+5x+x+5)=0\Rightarrow2(x^2+6x+5)=0\Rightarrow\\\\\boxed{2x^2+12x+10=0}

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