Question

Find a quadratic polynomial whose ine zero is 5 and product of zeroes is -18

Answer 1

Answer:

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Answer 2

Answer:

Required quadratic polynomial is $5 {x}^{2} - 7x - 18$

Step-by-step explanation:

Here given is one zero of quadratic polynomial is 5 and product of two zeros are -18.

So other zero is $\frac{ - 18}{5}$

Sum of zeroes $= 5 + ( - \frac{18}{5} ) = \frac{7}{5}$

If we know addition of zeroes and product of zeroes then easily we can find the quadratic polynomial.

For example,

Let the sum of zeroes be 5 and product of zeroes be (-2) of any quadratic polynomial.

Let one zero be a and another root be b.

So,$(a + b) = 5$and $ab= - 2$

Now equation is ${x}^{2} - (a + b)x + ab = 0$

${x}^{2} - 5x + ( - 2) = 0$

${x}^{2} - 5x - 2 = 0$

So,${x}^{2} - 5x - 2$is the polynomial whose sum of zeroes is 5 and product is (-2).

Now we let p and q be the zeroes of equation whose sum of zeros is $\frac{7}{5}$and product of zeroes is (-18).

Therefore $p + q = \frac{7}{5}$

and $pq = - 18$

So, equation is ${x}^{2} - (p + q)x + pq = 0$

${x}^{2} - \frac{7}{5} x - 18 = 0 \\ 5 {x}^{2} - 7x - 90 = 0$

So required polynomial is $5 {x }^{2} - 7x - 18$.