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.