Question

if a and b are zeros of polynomial p(x) 3x square -12x+15find the value of a square +b square

Answer 1

Answer:

Step-by-step explanation:

P(x)=3x²-12x-15

a and b are zeros of P(x), let us find the zeros

3x²-12x-15=0

(x+1)(x-5)=0

Thus x=5, -1

Zeros of P(x) are 5 and (-1)

Let a be 5

a²=25

Let b be (-1)

b²=1

a²+b²=26

Answer 2

The value is 6

Step-by-step explanation:

We are given the following quadratic equation in the question:

$p(x) = 3x^2 -12x + 15$

a and b are the roots of the quadratic equation.

Formula:

$ax^2 + bx + c = 0\\\\x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$p(x) = 3x^2 -12x + 15 = 0\\\\x = \dfrac{12 \pm \sqrt{(-12)^2-4(3)(15)}}{6}\\\\x = \dfrac{12\pm \sqrt{-36}}{6}\\\\x = \dfrac{12\pm 6\sqrt{-1}}{6}\\\\x = 2 + i, 2 -i\\a = 2 + i\\b = 2-i$

Evaluating:

$a^2 + b^2 \\=(2+i)^2 + (2-i)^2\\=4 + i^2 + 4i + 4 + i^2 - 4i\\=8 + 2i^2\\=8 + 2(-1)\\=6$

#LearnMore

If alpha and beta are the zeros of polynomial x^2 -x +1, find the value of alpha ^2 +β^2​

https://brainly.in/question/9560630