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Solve the equation below by factorising. 2p²7p+3=0​

Solve the equation below by factorising. 2p²7p+3=0​-example-1
User Jgrant
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2 Answers

7 votes

Final answer:

To solve the quadratic equation 2p² + 7p + 3 = 0 by factorisation, we find that the factors (2p + 1)(p + 3) yield the solutions p = -½ and p = -3. We then check these solutions to confirm they satisfy the original equation.

Step-by-step explanation:

The provided equation seems to contain a typo, but the intended quadratic equation appears to be in the form 2p² + 7p + 3 = 0. Solving quadratic equations through factorisation involves finding two binomials that multiply to give the original quadratic equation. Assuming the equation is 2p² + 7p + 3 = 0, we look for factors of the form (ap + b)(cp + d) such that ad + bc equals the coefficient of p, which in this case is 7, and ac equals 2, and bd equals 3.

Through trial and error or systematic testing, we find that (2p + 1)(p + 3) multiplies out to give the original equation. Setting each factor equal to zero gives us the roots of the equation:

  • 2p + 1 = 0 → p = -½
  • p + 3 = 0 → p = -3

Thus, the solutions to the equation 2p² + 7p + 3 = 0 are p = -½ and p = -3.

It is always good practice to check the answer by substituting the solutions back into the original equation to ensure that they satisfy the equation.

User Erynn
by
7.8k points
5 votes

Answer:

p=1/2

p=3

Step-by-step explanation:

User Christophor
by
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