Ques. 28 Junk food is unhealthful food that is high in calories from sugar or fat, with little dietary fiber, protein, vitamins, minerals, or other important forms of nutritional value. A sample of few students have taken. If α be the number of students who take junk food, β be the number of students who take healthy food such that α>β and α and β are the zeroes of the quadratic polynomial f(x)= x2-7x+10, then answer the following questions. Name the type of expression of the polynomial in the statement? Quadratic ii) Linear iii) Cubic iv) bi-quadratic Find the number of students who take junk food. 5 ii) 2 iii) 7 iv) None of these Find the quadratic polynomial whose zeroes are -3 and 4. x2+4x+2 ii) x2-x-12 iii) x2-7x+12 iv) None of these If one zero of the polynomial x2-9x+14 is 7 then other zero is 5 ii) 2 iii) 7 iv) None of these Find the number of students who take healthy food 5 ii) 2 iii) 7 iv) None of these
Answers
EVALUATION
(i) Here the given polynomial is
f(x) = x² − 7x + 10
Since the highest power of its variable that appears with nonzero coefficient is 2
So the polynomial is quadratic polynomial
Hence the correct option is (a) Quadratic
(ii) For Zero of the polynomial
f(x) = x² − 7x + 10
We have
\sf{ {x}^{2} - 7x + 10 = 0 }x
2
−7x+10=0
\sf{ \implies \: {x}^{2} - 5x - 2x + 10 = 0 }⟹x
2
−5x−2x+10=0
\sf{ \implies \: (x - 5)(x - 2)= 0 }⟹(x−5)(x−2)=0
\sf{ \implies \:x = 5 \: ,\: 2}⟹x=5,2
Now it is given that α be the number of students who take the junk food,β be the number of students who take healthy food such that α > β and α and β are the zeroes of the quadratic polynomial f(x) = x² − 7x + 10
So α = 5 and β = 2
Hence the number of students who take junk food = 5
Hence the correct option is (a) 5
(iii) From calculation in (ii) we observe that
α = 5 and β = 2
Hence the number of students who take healthy food = 2
Hence the correct option is (b) 2
(iv) The quadratic polynomial whose zeroes are -3 and - 4
\sf{ = {x}^{2} - ( - 3 - 4)x + ( - 3 \times - 4)}=x
2
−(−3−4)x+(−3×−4)
\sf{ = {x}^{2} + 7x + 12}=x
2
+7x+12
Hence the correct option is (d) None of these
(v) We find the zeroes of the quadratic polynomial x² − 5x + 6 as below
\sf{ {x}^{2} - 5x + 6 = 0}x
2
−5x+6=0
\sf{ \implies {x}^{2} -3x - 2x + 6 = 0}⟹x
2
−3x−2x+6=0
\sf{ \implies (x - 3)(x - 2) = 0}⟹(x−3)(x−2)=0
\sf{ \implies x = 3 \: , \: 2}⟹x=3,2
Thus two zeroes are 2 and 3
Since one given zero is 2
So other zero is 3
Hence the correct option is (d) None of these
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Answer:
Step-by-step explanation:EVALUATION
(i) Here the given polynomial is
f(x) = x² − 7x + 10
Since the highest power of its variable that appears with nonzero coefficient is 2
So the polynomial is quadratic polynomial
Hence the correct option is (a) Quadratic
(ii) For Zero of the polynomial
f(x) = x² − 7x + 10
We have
\sf{ {x}^{2} - 7x + 10 = 0 }x
2
−7x+10=0
\sf{ \implies \: {x}^{2} - 5x - 2x + 10 = 0 }⟹x
2
−5x−2x+10=0
\sf{ \implies \: (x - 5)(x - 2)= 0 }⟹(x−5)(x−2)=0
\sf{ \implies \:x = 5 \: ,\: 2}⟹x=5,2
Now it is given that α be the number of students who take the junk food,β be the number of students who take healthy food such that α > β and α and β are the zeroes of the quadratic polynomial f(x) = x² − 7x + 10
So α = 5 and β = 2
Hence the number of students who take junk food = 5
Hence the correct option is (a) 5
(iii) From calculation in (ii) we observe that
α = 5 and β = 2
Hence the number of students who take healthy food = 2
Hence the correct option is (b) 2
(iv) The quadratic polynomial whose zeroes are -3 and - 4
\sf{ = {x}^{2} - ( - 3 - 4)x + ( - 3 \times - 4)}=x
2
−(−3−4)x+(−3×−4)
\sf{ = {x}^{2} + 7x + 12}=x
2
+7x+12
Hence the correct option is (d) None of these
(v) We find the zeroes of the quadratic polynomial x² − 5x + 6 as below
\sf{ {x}^{2} - 5x + 6 = 0}x
2
−5x+6=0
\sf{ \implies {x}^{2} -3x - 2x + 6 = 0}⟹x
2
−3x−2x+6=0
\sf{ \implies (x - 3)(x - 2) = 0}⟹(x−3)(x−2)=0
\sf{ \implies x = 3 \: , \: 2}⟹x=3,2
Thus two zeroes are 2 and 3
Since one given zero is 2
So other zero is 3
Hence the correct option is (d) None of these