CASE STUDY QUESTION 6-Class X-Maths

CASE STUDY QUESTION 6-Class X-Maths

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:

(a) Name the type of expression of the polynomial in the above statement?
(i) quadratic (ii) cubic (iii) linear (iv) bi-quadratic
Ans: (i) quadratic

(b) Find the number of students who take junk food.
(i) 5 (ii) 2 (iii) 7 (iv) None of these

Ans: Now, f(x) = x² – 7x + 10 = 0
⇒ x² – 5x – 2x + 10 = 0
⇒ x(x – 5) – 2(x – 5) = 0
⇒(x – 5)(x – 2) = 0
⇒ x = 5, 2

(c) Find the number of students who take healthy food.
(i) 5 (ii) 2 (iii) 7 (iv) None of these

Ans: 2, 5

(d) Find the quadratic polynomial whose zeros are -3 and -4.
(i) x² + 4x + 2 (ii) x² – x – 12
(iii) x² – 7x + 12 (iv) None of these
Ans: (iv)

(e) If one zero of the polynomial x² – 5x + 6 is 2 then find the other zero.
(i) 6 (ii) -6 (iii) 2 (iv) None of these

Ans: (iv)