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) = x ^{2} – 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) = x^{2} – 7x + 10 = 0

⇒ x^{2} – 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) x^{2} + 4x + 2 (ii) x^{2 }– x – 12

(iii) x^{2} – 7x + 12 (iv) None of these

**Ans:** (iv)

**(e) If one zero of the polynomial x ^{2} – 5x + 6 is 2 then find the other zero.**

(i) 6 (ii) -6 (iii) 2 (iv) None of these

**Ans:** (iv)

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