Answer:
i) Equation can have exactly 2 zeroes.
ii) Both the zeroes will be real and distinctive.
Step-by-step explanation:
[tex]x^{2} - 7x + 3[/tex] is the given equation.
It is of the form of quadratic equation [tex]a^{2} + bx + c[/tex] 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 = [tex]b^{2} - 4ac = (-7)^{2} - 4(1)(3) = 49 - 12 = 37[/tex]
⇒ D = 37
Here, since D > 0, So both the roots will be real and distinctive.
