Question

If a and b are the zeros of the polynomial f(x)= 2x²- 7a +3 find the value of a²+ b²

Answer 1

Answer:

37/4

Step-by-step explanation:

$2x ^{2} - 7x + 3 \\ 2x ^{2} - 6x -x + 3 \\ 2 x(x - 3) - (x - 3) \\( 2x - 1)(x - 3)$

Therefore, a and b are

$\frac{1}{2} and \: 3$

respectively

Now

${a}^{2} + b ^{2} = \frac{1}{2} ^{2} + {3}^{2} \\ = \frac{1}{4} + 9 \\ = \frac{1}{4} + \frac{36}{4} \\ = \frac{37}{4}$

Answer 2

Answer:

37/4

Step-by-step explanation:

\begin{gathered}2x ^{2} - 7x + 3 \\ 2x ^{2} - 6x -x + 3 \\ 2 x(x - 3) - (x - 3) \\( 2x - 1)(x - 3)\end{gathered}

2x

2

−7x+3

2x

2

−6x−x+3

2x(x−3)−(x−3)

(2x−1)(x−3)

Therefore, a and b are

\frac{1}{2} and \: 3

2

1

and3

respectively

Now

\begin{gathered} {a}^{2} + b ^{2} = \frac{1}{2} ^{2} + {3}^{2} \\ = \frac{1}{4} + 9 \\ = \frac{1}{4} + \frac{36}{4} \\ = \frac{37}{4} \end{gathered}

a

2

+b

2

=

2

1

2

+3

2

=

4

1

+9

=

4

1

+

4

36

=

4

37