a, The value of p is 6 and 2/9
b. After solving the equation x is equal to 9
a. If the roots of a quadratic ax² + bx = c = 0, are equal then the discriminant is zero express as
b² - 4ac = 0
W have given the equation x² + 3px + (14p - 3) = 0
Here, a = 1
b = 3p
c = 14p - 3
So, substitute the value and we get
⇒ (3p)² - 4(14p -3) = 0
⇒ 9p² - 56p + 12 = 0
⇒ 9p² - 2p - 54p + 12
⇒ p(9p - 2) -6(9p - 2)
⇒ (9p - 2)(p - 6)
⇒ p = 6, p = 2/9
b. Lets substitute p = x in x² + 3px + (14p - 3)
⇒ x² + 3(6)x + (14(6) - 3)
⇒ x² + 18x + (84 - 3)
⇒ x² + 18x + 81
⇒ x² + 9x + 9x + 81
⇒ x(x + 9) +9(x + 9)
⇒ (x + 9)(x + 0)
⇒ x = 9
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