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Form quadratic equation whose roots are ...

Form quadratic equation whose roots are :
2,5

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To form a quadratic equation whose roots are given as 2 and 5, we can follow these steps: ### Step 1: Identify the roots The roots of the quadratic equation are given as: - \( r_1 = 2 \) - \( r_2 = 5 \) ### Step 2: Calculate the sum of the roots The sum of the roots \( S \) can be calculated as follows: \[ S = r_1 + r_2 = 2 + 5 = 7 \] ### Step 3: Calculate the product of the roots The product of the roots \( P \) can be calculated as follows: \[ P = r_1 \times r_2 = 2 \times 5 = 10 \] ### Step 4: Use the standard form of a quadratic equation The standard form of a quadratic equation based on its roots is given by: \[ x^2 - (S)x + P = 0 \] Substituting the values of the sum and product of the roots into this equation: \[ x^2 - (7)x + 10 = 0 \] ### Step 5: Write the final quadratic equation Thus, the quadratic equation whose roots are 2 and 5 is: \[ x^2 - 7x + 10 = 0 \] ### Summary of the solution The quadratic equation formed is: \[ x^2 - 7x + 10 = 0 \] ---
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