Construct and simplify equation whose root are -3,1

Biology

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Answer

x2+2x−3=0x^2 + 2x - 3 = 0

Step-by-step solution

5 steps

  1. Identify the given roots.

    The roots are r1=−3r_1 = -3 and r2=1r_2 = 1.

  2. Calculate the sum of the roots.

    Sum of roots=r1+r2=−3+1=−2\text{Sum of roots} = r_1 + r_2 = -3 + 1 = -2

  3. Calculate the product of the roots.

    Product of roots=r1×r2=(−3)×(1)=−3\text{Product of roots} = r_1 \times r_2 = (-3) \times (1) = -3

  4. Construct the quadratic equation using the formula x2−(sum of roots)x+(product of roots)=0x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0.

    x2−(−2)x+(−3)=0x^2 - (-2)x + (-3) = 0

  5. Simplify the equation.

    x2+2x−3=0x^2 + 2x - 3 = 0
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