Question

find a quadratic polynomial whose sum and zeroes are :-
(a) 5 and 17
(b) 0 and √15​

Answer 1

Answer:

$a) \: sum \: of \: zeroes \: = 5 \\ \frac{ - b}{a} = 5 \\ product \: of \: zeroes \: = 17 \\ \frac{c}{a} = 17 \\ required \: \: p(x) = {x}^{2} - 5x + 17 \\ b) \: sum \: of \: zeroes \: = 0 \\ \frac{ - b}{a} = 0 \\ product \: of \: zeroes \: = \sqrt{15} \\ \frac{c}{a} = \sqrt{15} \\ required \: p(x) = {x}^{2} + \sqrt{15}$

Answer 2

Given:-

a)↓

→α+β=5[Sum of Zeros]

→αβ=17[Product of Zeros]

b)↓

→α+β=0

→αβ=√15

$\rule{200}{1}$

To Find:-

→Quadratic Polynomial, Using Quadratic Formula?

$\rule{200}{1}$

AnsWer:-

★Quadratic Formula★

๛k[x²-(α+β)x+αβ]

$\rule{200}{1}$

a)↓

→k[x²-(5)x+17]

→k[x²-5x+17]

•Let k=1•

→1[x²-5x+17]

→x²-5x+17 (is the required Polynomial)

$\rule{200}{1}$

b)↓

→k[x²-(0)x+√15]

→k[x²+√15]

•Let k=1•

→1[x²+√15]

→x²+√15 (is the Required Polynomial)

$\rule{200}{2}$