Question

find a quadratic polynomial, the sum and the product of whose zeroes are √5 and ¾ respectively​

Answer 1

Answer: 4x^2 + 4$\sqrt{5$x + 3 = 0

Step-by-step explanation:

Let the two zeroes of the polynomial be a and b,

then as given in question,

a+b=  $\sqrt5$

ab = 3/4

We know that an equation can be formed when their sum and product of zeroes are given by the formula:

x^2 + (a+b)x + ab = 0

So, now substituting,

x^2 + ($\sqrt{5$)x + 3/4 = 0

x^2 + $\sqrt{5$x + 3/4 = 0

Now, multiplying the whole equation with 4 to eliminate four in the denominator of 3/4( this makes the equation simpler).

4x^2 + 4$\sqrt{5$x + 3 = 0 -------------------------- ANSWER.

Hope it helped,

Thanks.