Question

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Answer 1

Answer:

i) Equation can have exactly 2 zeroes.

ii) Both the zeroes will be real and distinctive.

Step-by-step explanation:

$x^{2} - 7x + 3$ is the given equation.

It is of the form of quadratic equation $a^{2} + bx + c$ and highest degree of the polynomial is 2.

Now, FUNDAMENTAL THEOREM OF ALGEBRA

If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.

So, the equation can have exact 2 zeroes (roots).

Also, find discriminant D = $b^{2} - 4ac = (-7)^{2} - 4(1)(3) = 49 - 12 = 37$

⇒ D = 37

Here, since D > 0, So both the roots will be real and distinctive.