Question

If ⅔

and -3 are the roots the equation px2

+ 7x +q = 0, find the values of p and q.​

Answer 1

Answer:

p = 3 & q = -6

Step-by-step explanation:

Given :

2/3 and -3 are the roots the equation px² + 7x + q = 0

To find :

the values of p and q

Solution :

Relation between zeroes and coefficients of a quadratic equation :

• Sum of zeroes = -(x coefficient)/x² coefficient
• Product of zeroes = constant term/x² coefficient

For the given quadratic equation px² + 7x + q = 0 :

• x² coefficient = p
• x coefficient = 7
• constant term = q

⇒ Sum of zeroes = -7/p

    $\sf \dfrac{2}{3}+(-3)=\dfrac{-7}{p} \\\\ \sf \dfrac{2-9}{3}=\dfrac{-7}{p} \\\\ \sf \dfrac{-7}{3}=\dfrac{-7}{p} \\\\ \longrightarrow \sf p=3$

⇒ Product of zeroes = q/p

  $\sf \dfrac{2}{3} \times (-3)=\dfrac{q}{3} \\\\ \sf -2=\dfrac{q}{3} \\\\ \sf q=-2 \times 3 \\\\ \longrightarrow \sf q=-6$

Therefore, p = 3 and q = -6